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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: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...respectively : shew that each of the angles ZXY, ZDY is equal to the angle BAC. 5. In a right.angled triangle, if a perpendicular be drawn from the right angle to the hypotenuse, the two triangles thus formed are equiangular to one another. 6. In a right'angled triangle...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893 - 800 pages
...times the angle in the other. 4. Inscribe a regular hexagon in a given circle. 5. 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. Cut a given straight line in extreme and mean ratio. IM ALGEBRA....
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893 - 804 pages
...times the angle in the other. 4. Inscribe a regular hexagon in a given circle. 5. 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. Cut a given straight line in extreme and mean ratio. IM ALGEBRA....
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Lectures in the Lyceum Or Aristotle's Ethics for English Readers

Aristotle - Ethics - 1897 - 440 pages
...be only three visible to the eye, while there are four present to I the mind. Thus in a right-angled triangle if a perpendicular be drawn from the right angle to the base, it could be shown that this perpendicular is a mean proportional between the segments of the base....
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...on the same side of it, prove that the pentagon is wholly within the hexagon. 11. In a right.angled triangle, if a perpendicular be drawn from the right angle to the base, prove that the triangles on each side of it are similar to the whole triangle, and to one another....
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Annual Report of the Commissioners ..., Volume 67

1901 - 490 pages
...which joins the middle points of these two sides will bisect the figure. Prove. 10. In a right-angled triangle if a perpendicular be drawn from the right angle to the hypotenuse, the square on either of the other sides is equal to the rectangle contained by the hypotenuse...
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Euclid, Book 1

Euclid, Rupert Deakin - Geometry - 1903 - 212 pages
...double the other acute angle, the hypotenuse will be double one of the sides. 44. In a right-angled triangle if a perpendicular be drawn from the right angle to the hypotenuse, it will divide the triangle into two triangles which are equiangular to one another and...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 484 pages
...THEOREM. In a right-angled triangle, if a perpendicular is drawn from the right angle to the hypotenuse, the triangles on each side of it are similar to the whole triangle and to one another. B DC Let BAC be a triangle right-angled at A, and let AD be drawn perp....
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Books 3-9

Euclid - Mathematics, Greek - 1908 - 456 pages
...ADC. [vi. Def. i] Therefore etc. PORISM. From this it is clear that, if in a right-angled triangle a perpendicular be drawn from the right angle to the base, the straight line so drawn is a mean proportional between the segments of the base. QED Sim.son remarks...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908 - 228 pages
...the other pair are either equal or supplementary .... (Euc. VI. 7) 421 BT. 3. — In a right-angled triangle, if a perpendicular be drawn from the right angle to the hypotenuse, the two triangles so formed are similar to the whole triangle and to each other (Euc. VI....
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