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" 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. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 92
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...unnecessarily prolix. K 3 PROPOSITION VIII. THEOREM. In a right-angled triangle (ABC), if a perpendicular (AD) be drawn from the right angle to the base; the triangles on each side of it are similar to the whole triangle, aud to one another. DEMONSTRATION. Because the angles BAG and ADB are equal, being both right...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...about a given triangle. 9. Give Euclid's definition of proportional magnitudes. 10. In a right-angled triangle, if a perpendicular be drawn from the right...angle to the base, the triangles on each side of it shall be similar to the whole triangle and to one another. To what objection has this definition been...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 318 pages
...triangle ABC may be proved to be 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 tc the base ; the triangles on each side of it are similar to the whole triangle, and to one another....
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...other pair of homologous gides are either equal or supplementary. PROP. VIIL THEOREM. In a right-angled triangle, if a perpendicular be drawn from the right angle to the opposite side, tin triangles on each side of the perpendicular tire similar to the whole triangle,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 318 pages
...PROP. VIII. THEOR. In. a rigid angled triangle if a perpendicular be drawn from the right angle tc the base ; the triangles on each side of it are similar to t/ie whale triangle, and to one another. Let ABC be a right angled triangle, having the right angle...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...and the part of it without the circle, shall be equal to the square of the line which touches it. 2. In a right angled triangle if a perpendicular be drawn...triangles on each side of it are similar to the whole triangle, and to one another. 3. Find the sum of n terms of the arithmetical progression 1, 3, 5, 7,...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - 1859
...triangles are one to another in the duplicate ratio of their homologous sides. C. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle and to one another. 6. EXERCISES IN GEOMETRY. I. 1. Trisect a given finite straight line....
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...triangle ABC may be proved to be equiangular to the triangle DEF, as in the first case. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and to one another. Given ABC a right-angled triangle, having the right angle. BAC ; and...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...unnecessarily prolix. PROPOSITION VIII. THEOREM. In a right-angled triangle (ABC), if a perpendicular (AD) 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. DEMONSTRATION. Because the angles BAC and ADB are equal, being both right...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...PROPOSITION VIII. THEOREM. • In a right-angled triangle, if a perpendicular be drawn from the rightanyle 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-triangle, having the right angle BAC; and from...
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