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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 Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...remaining || can be extracted exactly. THEOREM 3. In any right -angle triangle if a perpendicular le drawn from the right angle to the base the triangles on each side are similar to the whole triangle and to one another, and the perpendicular is a mean proportional...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...and have those angles equal about which the sides are proportionals. . . . . . . . . . . . . 215 8. In a right angled triangle, if a perpendicular be...triangles on each side of it are similar to the whole triangle and to one another. .. .. .. .. -.215 T1. To find a third proportional to two given straight...
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Examination Christmas,1875

Education Department,London - 1876
...alternate segments of the sides will be equal to the continued product of the other three segments. 3. In a right angled triangle, if a perpendicular be...triangles on each side of it are similar to the whole triangle and to one another. Write down some of the proportions that can be established between the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...have the same ratio which the other sides of the triangle have to one another. 4. 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. 5. If four straight lines be proportionals, the similar rectilineal figures...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1876 - 242 pages
...Def. 1. PROPOSITION VIIL THEOREM. In a right-angled triangle (ABC), i/ a perpendicular (AD) be dratcn 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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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878 - 228 pages
...and the base produced is equal to the perpendicular altitude of the triangle. 6. 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. Prove that the segments of the base are to one another in the duplicate...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...straight line &c. QED Cor. The angle in a semicircle is a right angle. PROP. xxv. THEOREM. (E. 6. 8). In a right angled triangle if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are similar to the whole triangle, and...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879
...of four magnitudes said to have the same ratio to the second which the third has to the fourth ? 7. In a right angled triangle, if a perpendicular be...triangles on each side of it are similar to the whole triangle and to one another. 8. Draw a straight line perpendicular to a given straight line of unlimited...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...equals the common angle GBH, and DEF will be equal to ABC. Proposition 8. Theorem.—In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side are similar to the whole triangle and to each other. Let ABC be a right-angled triangle, having the...
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Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880
...about each of their angles, be proportionals, the triangles shall be equiangular. 7. 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. 8. Describe the three different systems of units by means of which the...
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