i[23] (1) In order that the whole matter may be put in a clearer light, I will make use of a single illustration as follows. (2) Three numbers are given—it is required to find a fourth, which shall be to the third as the second is to the first. (23:3) Tradesmen will at once tell us that they know what is required to find the fourth number, for they have not yet forgotten the rule which was given to them arbitrarily without proof by their masters; others construct a universal axiom from their experience with simple numbers, where the fourth number is self-evident, as in the case of 2, 4, 3, 6; here it is evident that if the second number be multiplied by the third, and the product divided by the first, the quotient is 6; when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. [/4] (1) Mathematicians, however, know by the proof of the nineteenth proposition ff Spinoza of the seventh book of Euclid, what numbers are propor-tionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but intuitively, without going through any process. [25] (1) In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. 1. (2) To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. 2. To collect in this way the differences, the agreements, and the oppositions of things. 3. To learn thus exactly how far they can or cannot be modified. 4. To compare this result with the nature and power of man. (4) We shall thus discern the highest degree of per-fection to which man is capable of attaining. [26] (1) We shall then be in a position to see which mode of perception we ought to choose. (2) As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. (3) We may, therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. (4) For simple hearsay cannot a�ect anyone whose understanding does not, so to speak, meet it halfway. [27] (1) The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. (2) Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. (3) Wherefore this mode also must be rejected. [28] (1) Of the third mode of perception we may say in a manner that it gives us A New Antiqua from FontFont the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we The fourth mode alone apprehends the adequate essence of a thing without danger of error. (2) This mode, therefore, must be the one which we chiefly employ. (3) How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously un-known? (4) I will proceed to explain. [31] (1) But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of work-manship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, complicated mechanisms which they now possess. (31:2) So, in like manner, the intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these opera-tions again fresh instruments, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.

E T H I C AOrdine Geometrico demonſtrata,

E·TIn quinque Partes Diſtincta,

in quibus agitur,

I. De Deo. II. De Naturâ & Origine Mentis. III. De Origine & Naturâ Affectuum. IV. De Servitute Humanâ, ſeu de Affectuum V. De Potentia Intellectus, ſeu de Liberta

Baruch Spinoza is widely considered to be one of the forefathers of the Enlightenment. His Ethics, published in 1677, sought to demonstrate the unity and perfection of reality, and proposed rational understanding as the highest human virtue. To support his philosophical writings, he worked as a lens-grinder. In both of his professions, he aimed for clarity.

And so does ff Spinoza. It is an elegant workhorse: crisp, sturdy, economical, and ver-satile. A classic and highly readable Antiqua, it was inspired by the rigor of mid-century German text faces like Trump Mediaval and the lucidity of Janson revivals like Monotype Ehrhardt. Its x-height and aperture are generous, though not exaggerated. Its proportions are compact and its contrast relatively low. Robust thin strokes and pronounced serifs and terminals make it suitable for setting in small sizes under challenging conditions, both in print and on the Web. Abruptly tapered junctures keep characters sharply defined and, in the heavier weights, create enlivening light traps. Caps are comparatively light and do not interrupt the flow of the line. The italic is narrow, angular, and upright, with a 9.5° slope. ff Spinoza’s intended virtues are firmness, modesty, and, above all, clarity.

ff Spinoza’s understated design makes it ideal for books and longer texts, but closer examination reveals distinctive details that suit it for advertising, branding, packaging, and other types of more highly flavored work. Its curves are subtly faceted, with extra corners and unexpectedly straight edges that add interest in display sizes and energy in text sizes.

a new antiqua

KielerWoche

18. bis 26. Juni 2011

Substantial shoulders join branches and bowls firmly to their stems, which helps avoid the ‘picket-fence’ effect sometimes created by daintier typefaces.

ff Spinoza includes a comprehensive set of diacritics providing support for more than 70 languages, from Afrikaans to Zulu. The Pro version supports more than 130 languages.

ąðəļŋǿþşßűÿƶEach of the eight fonts includes small caps and eight types of figures: proportional old-

style, tabular oldstyle, proportional lining, tabular lining, numerator, denominator, superior, and inferior. Tabular figures are uniform in width across all weights to aid in the setting of columnar matter.

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$1234567890 £1234567890In addition to the conventional Euro sign—a makeshift intended to minimize the flaws

of the original EU design—ff Spinoza includes a more rational (and compact) alternative: a double-crossbarred uppercase E. It can be accessed through Stylistic Set 1.

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features

mun

The following glyphs are included in all weights of ff Spinoza Pro:

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8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but intuitively,

9/11 without going through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature and power of man. We shall thus discern the highest degree of perfection to

10/12 which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustra-tion; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific

11/13 in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental proper-ties, which are never clearly understood, unless the essence of the things in question be known

12/14.5 first. wherefore this mode also must be rejected. Of the third mode of per- ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the

14/17 one which we chiefly employ. How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concern-ing things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these

18/21 were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more com-plex tools, and fresh feats of workmanship, till they arrived

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but intuitively, without going through any process. In order that from these modes of

9/11 perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature and power of man. We shall thus discern the highest degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the

10/12 first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the

11/13 idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it

12/14.5 is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, there- fore, must be the one which we chiefly employ. How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to

14/17 accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest opera-tions to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at devising

18/21 complicated mechanisms which they now possess. So, in like manner, the intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these operations again fresh instruments, or the power of pushing its

italicregular ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz & fiflðþß!?abcdefghijklmnopqrstuvwxyz1234567890$£¥€€ � 1234567890$£¥€€

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Idea of the idea Hence it is plain

2006Sauvignon Blanc

sonoma

In the summer of 1951, Larry and Miriam Colson bought eight acres

beside the swift, narrow stream where Larry had fished for steelheads as a boy,

raised two Army surplus Quonset huts, and planted their first vines.

Today, Spike River is one of the oldest family-run wineries in the Mayacamas

foothills. We’re especially proud of our Sauvignon Blanc: a big, rich,

well-oaked wine, with bright citrus notes giving way to a satiny finish,

it has a crisp minerality that springs from our chalky volcanic soil.

Spike River

Alc. 14.1% by Vol.

nowysystem009stodoła remix

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They see it not But intuitively

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition,

9/11 but IntuItIvely, without going through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature and power of man. We shall thus discern

10/12 the hIghest degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that

11/13 the certaInty arIsIng from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which

12/14.5 are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone

14/17 apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? I will proceed to explain. But as men at first made use of the instruments

18/21 supplIed by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportion-ality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but intuitively, without going through any

9/11 process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature and power of man. We shall thus discern the highest degree of perfection to which man is capable of attaining.

10/12 we shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. For simple hearsay cannot affect

11/13 anyone whose understandIng does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected.

12/14.5 of the thIrd mode of per ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we

14/17 avaIl ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to accomplish easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less

18/21 labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and to fresh feats of workmanship, till they finally arrived at making complicated mechanisms which

OrarioSFSM Circumv

A NapoliSorrento 5.01 5.37 6.07f 6.25 6.55d 7.22 7.38S. Agnello 5.03 5.39 6.09 6.27 6.57 7.24 7.40Vico 5.12 5.48 6.18 6.36 7.06 7.31 7.48C/Mare 5.21 5.57 6.27 6.45 7.14 7.39 7.57Pompeii 5.31 6.07 6.37 6.55 7.21 7.48 8.07Ercolano 5.49 6.25 6.55 7.13 7.36 8.07 8.26Napoli 6.08 6.44 7.14 7.32 7.46 8.27 8.44

A SorrentoNapoli 5.09f 5.39 6.09f 6.40d 7.09 7.39 8.11Ercolano 5.28 5.58 6.28 6.53 7.28 7.58 8.23Pompeii 5.47 6.17 6.47 7.07 7.47 8.17 8.37C/Mare 5.57 6.27 6.57 7.16 7.57 8.27 8.46Vico 6.06 6.36 7.06 7.24 8.06 8.36 8.54

such, that I shrunk almost from the thought of going away, even to travel, which is generally so much desired by young men. He roused me by manly and spirited conversation. He advised me, when settled in any place abroad, to study with an eagerness after knowledge, and to apply to Greek an hour every day; and when I was moving about, to read diligently the great book of mankind.

On Wednesday, August 3, we had our last social meeting at the Turk’s Head coffee- house, before my setting out for foreign parts. I had the misfortune, before we parted, to irritate him unintentionally. I mentioned to him how common it was in the world to tell absurd stories of him, and to ascribe to him very strange sayings. Johnson. ‘What do they make me say, Sir?’ Boswell. ‘Why, Sir, as an instance very strange indeed (laughing heartily as I spoke,) David Hume told me, you said that you would stand before a battery of cannon, to restore the Convocation to its full powers.’ Little did I apprehend that he had actually said this: but I was soon convinced of my errour; for, with a determined look he thundered out, ‘And would I not, Sir? Shall the Presbyterian Kirk of Scotland have its General Assembly, and the Church of England be denied its convocation?’ He was walking up and down the room while I told him the anecdote; but when he uttered this explosion of high-church zeal, he had come close to my chair, and his eyes flashed with indignation. I bowed to the storm, and diverted the force of it, by leading him to expatiate on the influence which religion derived from maintaining the church with great external respectability.⁵

On Friday, August 5, we set out early in the morning in the Harwich stage coach. A fat elderly gentlewoman, and a young Dutchman, seemed the most inclined among us to conversation. At the inn where we dined, the gentlewoman said that she had done her best to educate her children; and particularly, that she had never suffered them to be a moment idle. Johnson. ‘I wish, madam, you would educate me too; for I have been an idle fellow all my life.’ ‘I am certain, Sir, (said she) you have not been idle. Johnson. ‘Nay, Madam, it is very true; and that gentleman there (pointing to me,) has been idle. He was idle at Edinburgh. His father sent him to Glasgow, where he co

{132}

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For we possess Circumference

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of

9/11 euclId’s proposItIon, but intuitively, without going through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature

10/12 and power of man. We shall thus discern the highest degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncer-tain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustra-tion; now one can only arrive at knowledge of a thing through knowledge of its essence, as will

11/13 hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of percep-tion cannot be said to give us the idea of the proportion of which we are in search. More-over its results are very uncertain and indefinite, for we shall never discover anything in

12/14.5 natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient

14/17 to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things

18/21 prevIously unknown? I will proceed to explain. But as men at first made use of the instruments sup-plied by nature to accomplish very easy pieces of work-manship, laboriously and imperfectly, and then, when these were done, wrought other things more difficult

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but

9/11 IntuItIvely, wIthout goIng through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with the nature and power of man. We shall thus discern the

10/12 hIghest degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that the certainty

11/13 arIsIng from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly

12/14.5 understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it gives us the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of

14/17 a thIng wIthout danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to accomplish very easy

18/21 pIeces of workmanshIp, laboriously and imper-fectly, and then, when these were completed, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making

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8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it

9/11 not by vIrtue of Euclid’s proposition, but intuitively, without going through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to per- fect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppositions of things. To learn thus exactly how far they can or cannot be modified.

10/12 to compare thIs result with the nature and power of man. We shall thus discern the high- est degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a

11/13 thIng through knowledge of its essence, as will hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very

12/14.5 uncertaIn and IndefInIte, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it does give us the idea of the thing sought, and that it

14/17 enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we avail ourselves

18/21 of It so as to gain the fourth kind of knowledge with the least delay concerning things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship,

8/10 when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. Mathematicians, however, know by the proof of the nineteenth proposition of the seventh book of Euclid, what numbers are proportionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of

9/11 euclId’s proposItIon, but intuitively, without going through any process. In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. To collect in this way the differences, the agreements, and the oppo- sitions of things. To learn thus exactly how far they can or cannot be modified. To compare this result with

10/12 the nature and power of man. We shall thus discern the highest degree of perfection to which man is capable of attaining. We shall then be in a position to see which mode of perception we ought to choose. As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is mani-fest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its

11/13 essence, as wIll hereafter appear. We may therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. For simple hearsay cannot affect anyone whose understanding does not, so to speak, meet it halfway. The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. Moreover its results are very uncertain and indefinite, for we shall never

12/14.5 dIscover anythIng in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. Wherefore this mode also must be rejected. Of the third mode of per ception we may say in a manner that it does give us the idea of the thing sought, and that it enables us to draw conclusions without risk of error;

14/17 yet It Is not by itself sufficient to put us in possession of the perfection we aim at. The fourth mode alone apprehends the adequate essence of a thing without danger of error. This mode, therefore, must be the one which we chiefly employ. How, then, should we avail our-selves of it so as to gain the fourth kind of knowledge with the least

18/21 delay concernIng things previously unknown? I will proceed to explain. But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and im-perfectly, and then, when these were finished, wrought

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i[23] (1) In order that the whole matter may be put in a clearer light, I will make use of a single illustration as follows. (2) Three numbers are given—it is required to find a fourth, which shall be to the third as the second is to the first. (23:3) Tradesmen will at once tell us that they know what is required to find the fourth number, for they have not yet forgotten the rule which was given to them arbitrarily without proof by their masters; others construct a universal axiom from their experience with simple numbers, where the fourth number is self-evident, as in the case of 2, 4, 3, 6; here it is evident that if the second number be multiplied by the third, and the product divided by the first, the quotient is 6; when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional. [/4] (1) Mathematicians, however, know by the proof of the nineteenth proposition ff Spinoza of the seventh book of Euclid, what numbers are propor-tionals, namely, from the nature and property of proportion it follows that the product of the first and fourth will be equal to the product of the second and third: still they do not see the adequate proportionality of the given numbers, or, if they do see it, they see it not by virtue of Euclid’s proposition, but intuitively, without going through any process. [25] (1) In order that from these modes of perception the best may be selected, it is well that we should briefly enumerate the means necessary for attaining our end. 1. (2) To have an exact knowledge of our nature which we desire to perfect, and to know as much as is needful of nature in general. 2. To collect in this way the differences, the agreements, and the oppositions of things. 3. To learn thus exactly how far they can or cannot be modified. 4. To compare this result with the nature and power of man. (4) We shall thus discern the highest degree of per-fection to which man is capable of attaining. [26] (1) We shall then be in a position to see which mode of perception we ought to choose. (2) As to the first mode, it is evident that from hearsay our knowledge must always be uncertain, and, moreover, can give us no insight into the essence of a thing, as is manifest in our illustration; now one can only arrive at knowledge of a thing through knowledge of its essence, as will hereafter appear. (3) We may, therefore clearly conclude that the certainty arising from hearsay cannot be scientific in its character. (4) For simple hearsay cannot a�ect anyone whose understanding does not, so to speak, meet it halfway. [27] (1) The second mode of perception cannot be said to give us the idea of the proportion of which we are in search. (2) Moreover its results are very uncertain and indefinite, for we shall never discover anything in natural phenomena by its means, except accidental properties, which are never clearly understood, unless the essence of the things in question be known first. (3) Wherefore this mode also must be rejected. [28] (1) Of the third mode of perception we may say in a manner that it gives us A New Antiqua from FontFont the idea of the thing sought, and that it enables us to draw conclusions without risk of error; yet it is not by itself sufficient to put us in possession of the perfection we The fourth mode alone apprehends the adequate essence of a thing without danger of error. (2) This mode, therefore, must be the one which we chiefly employ. (3) How, then, should we avail ourselves of it so as to gain the fourth kind of knowledge with the least delay concerning things previously un-known? (4) I will proceed to explain. [31] (1) But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of work-manship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, complicated mechanisms which they now possess. (31:2) So, in like manner, the intellect, by its native strength, makes for itself intellectual instruments, whereby it acquires strength for performing other intellectual operations, and from these opera-tions again fresh instruments, or the power of pushing its investigations further, and thus gradually proceeds till it reaches the summit of wisdom.