Short, but yet plain elements of geometry. Shewing how by a brief and easie method, most of what is necessary and useful in Euclid, Archimedes, Apollonius, and other excellent geometricians, both ancient and modern, may be understood / Written in French by F. Ignat. Gaston Pardies. And render'd into English, by John Harris.

Ignace-Gaston Pardies

Date:: 1725

Credit: Short, but yet plain elements of geometry. Shewing how by a brief and easie method, most of what is necessary and useful in Euclid, Archimedes, Apollonius, and other excellent geometricians, both ancient and modern, may be understood / Written in French by F. Ignat. Gaston Pardies. And render'd into English, by John Harris. Source: Wellcome Collection.

39/184 page 27

$2. The Angle o dd is equal to c d b (1. 31.) and e Side 6d is common to both thefe Triangles; wherefore the Triangle o b d is equal toc d b (by Lora.) | _ 9. In every Parallelogram, the oppofite Sides are lways equal. | | For (drawing the Diagonal db) the whole Trian- le do b will be equal to the Triangle be d, by the pregoing Prop. And confequently, theSide c 4 muft e equal to o 6, and the Side o d toc b. 10. Two Diagonals,ac and b d do, biffe& each ither in the middle at e. For ia therwoTriangles aedand bec,the Sidead 5 equal todc (3. 9.) The Angle e a dis equal to ecd 1.31.) and moreover the (Vertical) angles ed and ce bare equal alfo L. 23.) Wherefore the whole Triangle (ed zs refpeétively equal to the Trian= le bec (2. 14.) And confequently, e Side de isequaltoe b, and the Side ae to the ide ec. The two Diagonals therefore biffeét each cher in the middle. Q.E.D. 11. Every Righc Line, as f g, pafling through the hiddle of a Diagonal, divides the Parallelogram nto two equal Parts. To demonftrate which,the Trapezium or Irregular Quadrilateral Figure fg d a muft be proved equal to ne Trapezium fg cb. And that is thus done. 1. The -riangle bef is equal tothe Triangle deg: For the ide de is equal toed by the Suppofi- | ion; and the Angle ef b is equal to pet Ba 4 ig d (1. 31.) and the oppofire Angles De] ite areequal ;whereforetheTriangle g . C jf b is equal to edg (2. 14.) 2. The & : treat Triangle abd is equal to bdc (3. 8.) wherefore { from the Triangle 2 » d you take away the little Triangle fe b, and inftead of ir put the Triangle e dg | 30 (which Au$

Licence and re-use

Contents