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... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
A Supplement to the Elements of Euclid - Page 296
by Daniel Cresswell - 1819 - 410 pages

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...also cuts the base produced; the segments between the dividing line and the extremities of the base have the same ratio which the other sides of the triangle have to one another : and if the segments of the base produced, have the same ratio which the other sides...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...also cuts the base produced, the segments between the bisecting line and the extremities of the base have the same ratio which the other sides of the triangle have to each other ; and if the segments of the base produced have the same ratio which the other sides...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 554 pages
...cut into two equal angles by the straight line AD. Therefore, if the angle, &c. QED PROP. A. THEOR. IF the outward angle of a triangle made by producing...the other sides of the triangle have, the straight lme drawn from the vertex to the point of section divides the outward angle of the triangle into two...

Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...”oto tiro rqnal angles, by a straight line »liich also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have to one another : and if the seginenU of the b.ise have the same ratio which the other sides of the...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...same ratio which the other sides of the triangle have to one another : And if the segments of the base have the same ratio which the other sides of the triangle have to one another, the straight line drawn from the vertex to the point of section, divides the vertical...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...a triangle be bisected by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another : Andifthe segments of the basiJiave ihe same ratio -ahich the other sides of the triangle...

Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...also cuts the base produced, the segments between the bisecting line and the extremities of the base, have the same ratio which the other sides of the triangle have to one another. Shew that the converse is also true. 2. Equiangular parallelograms have to one another...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...a/so cuts the base produced ; the segments bijjeen the dividing line and the extremities of the base have the same ratio which the other sides of the triangle have to one another: And if the segments of the base produced, have the same ratio which the other sides...