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Books Books 1 - 10 of 96 on IN a right-angled triangle, if a perpendicular be drawn from the right angle to the....  
" IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. "
Books 3-9 - Page 209
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...first case. Therefore, if two triangles, &c. QED PROP. VIII. THEOR. IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to each other* Let ABC be a right angled...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...Wherefore, if two triangles, &c. QED G D 5.1. F PROP. VIII. THEOR. See N IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...angles equal about which the sities are proportionals. Prop. VllI.Thcor. In a right angled triangle, if a perpendicular be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, and to one another. Prop. IX. Prob. From a given...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...Wherefore, if the two triangles, &c. Q . ED 5. I. PROP. VIII. THEOR. Se«N. IN a right angled triangle, if a perpendicular be drawn from the right angle to the base ; the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled...
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The mathematical questions, proposed in the Ladies' diary, and ..., Volume 4

Thomas Leybourn - Mathematics - 1817
...14470-0735 feet, the mountain's height required. in. QUESTION 1211, by Mr. S. Titlow, of Härtesten. If, in a right-angled triangle, a perpendicular be drawn from the right angle upon the hypothenuse, and circles inscribed, within the two smaller triangles on each side of it, their...
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Geometrical problems deducible from the first six books of Euclid: arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...to the part produced the same ratio that the sum of the sides of the triangle has to the base. 29- If in a right-angled triangle, a perpendicular be drawn from the right angle to the hypothenuse, and circles inscribed within the triangles on each side of it ; their diameters will be...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 1819 - 377 pages
...BACD, FOGD being similar, and similarly situated, AD : OD :: AB + AC : FO + OG :: AB + AC : BC. (29.) If in a right-angled triangle, a perpendicular be drawn from the right angle to the hypothenuse, and circles inscribed within the triangles on each side of it ; their diameters will be...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Trigonometry - 1819 - 333 pages
...equiangular to the triangle DEF, as in the first case. PROP. VIII. THEOR. In a right angled triangle, if a perpendicular be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled...
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Elements of arithmetic, algebra and geometry

George Lees - 1826
...BD : : BD : BCC ; that is BD is a mean proportional between AB and BC. Which was to be found. Cor. If, in a right-angled triangle, a perpendicular be drawn from the right angle to the base, it is a mean proportional between the segments of the base ; the triangles on each side of it are similar...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid, Phillips - 1826 - 180 pages
...triangle DEF. If, therefore, two triangles, 8tc. QED PROPOSITION VIII. THEOREM. If in a right angled triangle a perpendicular be drawn from the right angle to the base, the triangles made by 'the perpendicular are similar to the whole and to one another. Let ABC be a right angled triangle,...
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