SUPPLEMENT TO THE PREFACE

...since this [proposition] is true along with "it is possible for none," and since it is not contained by that, it must be contained by "it is not possible for all," which is its negation. Thus, "necessity not for all," since it is not contained by "it is possible for none," must necessarily be contained by "it is not possible for none."

p. 481, lines 19—30 (folio 174 recto of Manuscript Y, folio 352 recto of Manuscript Z).
Lines 19—23: "For either in the first, or in the middle, or in the third" This is a lemma, or a snippet of the original text by Aristotle being commented upon. || Line 24: after "through" original: διὰ add "indeed" original: μὲν || after "this" original: ἤδε add "the woman" original: ἡ γυνὴ || Line 25: after "therefore" original: ἄρα add "the woman" original: ἡ γυνὴ || "This—line 26: has"] "and also through the second figure A 'figure' refers to the specific arrangement of terms in a logical syllogism., such as 'this woman is pale. Every pregnant woman is pale. Therefore, this woman is pregnant'" original: ἤδε ἡ γυνὴ ὠχρά. πᾶσα κυοῦσα ὠχρά. ἤδε ἄρα ἡ γυνὴ κύει. This is a classic Aristotelian example of an 'argument from signs.' || Line 27: "that through a sign"] "the example through the sign" || Line 28: "virtuous" [is used for] "wise" || Line 29: "furthermore."

Folio 94 recto of Manuscript Y, regarding the lemma (page 36a 22) "and it is not possible to lead to an impossibility," displays two scholia Scholia are explanatory comments written in the margins of manuscripts by later scholars., one of which has "by Philoponus John Philoponus (c. 490–570) was a Christian philosopher and scientist in Alexandria known for his commentaries on Aristotle. on the same [passage]" added to it. It begins: "That is, if it is assumed," and ends: "those things mentioned above." To the other part of this scholion, which begins: "It should also be stated thus" (with a red letter L original: $λ$ rubr.), the word "similar" is written in the margin. Manuscript Z contains this part of the scholion on folio 249 verso, but omits the name of Philoponus.

Folio 95 recto of Manuscript Y and folio 251 verso of Manuscript Z, regarding the lemma (page 36b 21) "except when the privative proposition of 'being possible' is placed according to 'belonging,'" A privative proposition is a negative statement, such as 'Some A is not B.' after a scholion by Magentenus Leo Magentenus was a 13th-century Byzantine monk and commentator on Aristotle's logic., a second one by John Philoponus is added, which begins: "Aristotle having reminded us," and ends: "that 'for none' is concluded by necessity." Likewise, on folio 98 verso of Manuscript Y and folio 268 verso of Manuscript Z, regarding the lemma (page 40b 25) "or from a hypothesis," a second scholion is inscribed, beginning: "It must be known that the so-called hypothetical syllogisms," and ending: "they are the judgments from there."

Folio 101 recto of Manuscript Y, regarding the lemma (page 41b 13) "but it becomes more clear in the diagrams, for example, that in an isosceles triangle the [angles] at the base are equal," the name of Philoponus is added to a scholion which begins: "That the [angles] at the base of an isosceles triangle are [equal]," and ends on folio 102 recto: "the remaining things will be entirely equal." Folio 270 recto of Manuscript Z displays the first part of this scholion up to the words: "and I shall set out the proofs of both, and let that of Euclid Euclid (c. 300 BCE) was the most famous mathematician of antiquity, author of the 'Elements.' lead the way as fundamental."

Folio 157 recto of Manuscript Y and folio 333 verso of Manuscript Z, regarding the lemma (page 65a 4): "which those who think they are drawing parallel lines do" [the word "drawing" is omitted in Z]. In the margin: "By Philoponus" (Z adds the abbreviation for "John").

It seems that in this way he is attacking Euclid, as Euclid was younger, if indeed Plato and Aristotle [lived before him], as Proclus Proclus (412–485 CE) was a Neoplatonist philosopher who wrote a famous commentary on the first book of Euclid's 'Elements.' says; and the Stagirite Aristotle, who was born in the city of Stagira. is not poorly suggesting here how he [Euclid] proves the case of parallel lines. But there were some contemporaries of Aristotle who thought they could prove the parallel lines through the following method. For they said: if the lines are parallel, the interior angles on the same side are equal to two right angles. For if the interior angles on the same side are not equal to two right angles, but are less, then the lines are not parallel, but will meet because of the geometrical postulate This refers to Euclid’s famous Parallel Postulate. which says: if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced infinitely, meet on that side where the angles are less than two right angles. If, therefore, it is not possible for the angles in parallel lines to be less than two right angles, nor can they be greater. For even in that way they will meet on the other side. It is necessary for them to be equal to two right angles.

If, then, the lines are parallel, the interior angles on the same side are equal to two right angles; for instance, if line $\bar{a}\bar{b}$ and line $\bar{g}\bar{d}$ are two parallel lines, and a straight line $\bar{e}\bar{z}$ has fallen upon them, then the interior angles on the same side, namely angles $\bar{b}\bar{h}\bar{t}$ and $\bar{h}\bar{t}\bar{d}$, are equal to two right angles for the reason stated. But if the interior angles on the same side are equal to two right angles, then the alternate angles $\bar{a}\bar{h}\bar{t}$ and $\bar{h}\bar{t}\bar{d}$ are equal to one another. For since angles $\bar{b}\bar{h}\bar{t}$ and $\bar{h}\bar{t}\bar{d}$ are equal to two right angles, and angles $\bar{a}\bar{h}\bar{t}$ and $\bar{b}\bar{h}\bar{t}$ are also equal to two right angles—according to the 8th theorem This actually refers to what we now know as Euclid's Book I, Proposition 13. of the first book of the Geometrical Works which says that whenever a straight line standing on a straight line makes angles, it will make either two right angles or angles equal to two right angles. For here too, the straight line $\bar{z}\bar{e}$ stood upon the straight line $\bar{a}\bar{b}$. Therefore, angles $\bar{a}\bar{h}\bar{t}$ and $\bar{b}\bar{h}\bar{t}$ are equal to angles $\bar{b}\bar{h}\bar{t}$ and $\bar{h}\bar{t}\bar{d}$, for both these and those are equal to two right angles; and if you take away equals from equals, the remainders are equal. Let the common angle $\bar{b}\bar{h}\bar{t}$ be taken away. The remaining angles $\bar{a}\bar{h}\bar{t}$ and $\bar{h}\bar{t}\bar{d}$ are therefore equal to each other, and they are alternate angles. If, then, the interior angles on the same side are equal to two right angles, the alternate angles are equal to one another. But if the alternate angles...