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" In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base. "
A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... - Page 160
by Thomas Malton - 1774 - 440 pages
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...BD-DC = AB3 + AC2 ( Prop. XXIX. ). Hence in an isosceles triangle the square of a side is equivalent to the square of any line drawn from the vertex to the base, together with the rectangle of the parts into which it divides the base ; and here again we are...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 368 pages
...in the points F, G, If, respectively; then AF. AB + AH. AD = AG.AC. 152. In any isSsceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base. 153....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 368 pages
...AD, in the points F, G, If, respectively; then ARAB + AH.AD = AG.AC. 152. In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base. 153....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1884 - 368 pages
...AD, in the points F, G, H, respectively; then ARAB + AH.AD = AG.AC. 152. In any isosceles triangle, the square of one of the equal sides is equal to the square of iny straight line drawn from the vertex to the base plus the product of the segments of the base. 153....
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A Short History of Greek Mathematics

James Gow - Mathematics - 1884 - 323 pages
...proposition that, if in an isosceles triangle a straight line be drawn from the vertex to the base, then the square of one of the equal sides is equal to the square of the straight line so drawn + the rectangle under the segments of the base3. (Simson adds a lemma to...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 398 pages
...contact is a mean proportional between the diameters of the circles. 601. In any isosceles triangle the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base, plus the product of the segments of the base. CONSTRUCTIONS....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1899 - 247 pages
...of a triangle are inversely proportional to the corresponding bases. 6. In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base. 7. The...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 473 pages
...intersect at D, show that ZB 2 - ,AC 2 = lu? - ~C&. Ex. 273. In an isosceles triangle, the square of a leg is equal to the square of any line drawn from the vertex to the base, increased by the product of the segments of the base. Ex. 274. The squares of two chords drawn...
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Plane Geometry

George Albert Wentworth - Geometry, Plane - 1899 - 256 pages
...the opposite sides intersect at D, show that Ex. 273. In an isosceles triangle, the square of a leg is equal to the square of any line drawn from the vertex to the base, increased by the product of the segments of the base. Ex. 274. The squares of two chords drawn...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 473 pages
...intersect at D, show that 1 - Zc2 = USD* - ~CD2. Ex. 273. In an isosceles triangle, the square of a leg is equal to the square of any line drawn from the vertex to the base, increased by the' product of the segments of the base. Ex. 274. The squares of two chords drawn...
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