Volume 2

The elements of Euclid explain'd. In a new, but most easie method, together with the use of every proposition through all parts of the mathematicks / Written in French, by that exccellent [sic] mathematician F. Claud. Francis Milliet de Chales ... And now carefully done into English. And purg'd from a multitude of errors, which had escap'd in the original.

Euclid

Date:: 1685

Credit: The elements of Euclid explain'd. In a new, but most easie method, together with the use of every proposition through all parts of the mathematicks / Written in French, by that exccellent [sic] mathematician F. Claud. Francis Milliet de Chales ... And now carefully done into English. And purg'd from a multitude of errors, which had escap'd in the original. Source: Wellcome Collection.

47/392 page 37

$into the angles AEC and CEB-equal ro two right ‘ones, (61 the 13.) In like manner the line. BE {falling upon che line CD, makes the angle CER land, BED equal το two night ones. Therefore μεις angles AEC, CEB, taken together; are e- wp Qual.co che angles CEB, BED; therefore taking wlaway che anele CEB from both, the angle AEC Will remain equal το DEB, (dy the 3. Maxime.) Γη], Gorall'1. IE cwolines DE, and EC , concur= (γης ac the fame point E of the line AB, form ig¢4fWith it che oppofice angles AEC, DEB equal, ΟΕ and EC make but ene right line, 1 Demonfiration, | The line EC falling upon the line AB, makes the angles AEC, and ΕΡΕ equal co two right ones, (Ly the 13.) Tis fuppos’d likewife that the angle DEB is equal to the angle AEC. iUherefore the angles DEB, BEC, are equal to Wo right ones. And (dy the 1.4.) the lines CE μιλά ED make burone right line, The USE, ] A © Thetwo preceding Propo- Σά “fitions are made ufe: of το ’ “prove, that two lines make sp; a “butione total. As for exam. | 4-73: plein Catoptricks or Perfpe- _» (© éyes,where char is required “to prove, that of all che lines | F thar$

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