The Elements of Euclid; With Select Theorems Out of Archimedes

The Elements of Euclid; With Select Theorems Out of Archimedes

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1727 edition. Excerpt: ... P 34. FI, asCLS to SF(). Therefore BI is also to IF, M C F to OL. i.e. j ': ."-PROP. HI. Theorem; IF a right Line (B F) which biseSls an Angle of a JVg. Triangle, doth also cut the Base (A C), the Segments of the Base (AF, FC)-will have the same Proportion betwixt themselves as the Sides (A B, BC) have. And if the Parts of the Base (AF. FC) have the same Proportion betzuixt themselves, as the other Sides (A B, CB)the Line (BF) which cuts the Bafe, bifeBs the opposite Angle (A B C).. Part 1. Draw forth CB until BL be equal to B A; and join A L. Because in the Triangle Z the Sides L', B j A B, are equal, the Angles also (e) L and O are equal. M Per y. Because therefore the external Angle ABC is equal to ' the two internal ones (f) L, O, the Angle I, which byi()Perji. the Hypothesis is half ABC, will be equal to the Angle, 'L. Therefore A L, F B (g) are parallel. Therefore in %Per Part Part 2. Produce C B again until B L be equal to B A. Because A F is suppos'd to be to F C, as A B (that is, (z) 2 L B) is to B C j A L, F B (a) are parallel. Therefore X/t3'7' the external Angle I is equal to the internal one L( Jj and the alternate Q_equal to the alternate O. But bef-)M-.cause LB, AB, are equal, the Angles L and O (c) are equal. Therefore I and () are also equal. Therefore AB Cij bisected. QSTl. PROP. IV. Theorem: TRiangles which are equiangular to one another are like or similar, that is, have their Sides also (d') i' '6' that are opposite to the equal Angles proportional. &g.?. In the Triangles X, Z, let the Angle A be equal to the Angle F, and the Angle C to the Angle L, and the Angle B to the Angle I; I fay, that A B is to F I, as AC is to FL; and AC is to FL, as CBis toLI j and CB is to LI, as BA is to FI. E?"7,8, ...show more

Product details

  • Paperback | 74 pages
  • 189 x 246 x 4mm | 150g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236556232
  • 9781236556233