Elements of Geometry and Trigonometry |
From inside the book
Page 91
... similar triangles are to each other as the on their homologous sides . Let ABC , DEF , be two similar trian- gles , having the angle A equal to D , and the angle B - E . Then , first , by reason of the equal an- G gles A and D ...
... similar triangles are to each other as the on their homologous sides . Let ABC , DEF , be two similar trian- gles , having the angle A equal to D , and the angle B - E . Then , first , by reason of the equal an- G gles A and D ...
Page 92
... similar ( Prop . XX . ) ; therefore the angle BCA is equal to GHF . Take away these equal angles from the equal angles BCD , GHI , and there remains ACD = FHI . But since the triangles ABC , FGH , are similar , we have AC : FH : BC : GH ...
... similar ( Prop . XX . ) ; therefore the angle BCA is equal to GHF . Take away these equal angles from the equal angles BCD , GHI , and there remains ACD = FHI . But since the triangles ABC , FGH , are similar , we have AC : FH : BC : GH ...
Page 164
... similar triangles ABH , aBh , and of the similar parallelograms AC , ac , we have P D H B AH ah : AB : ab :: BC : bc . : But since the bases are similar , we have base BCD hence , a base bcd : BC2 : bc ( Book IV . Prop . XXV . ) ; base ...
... similar triangles ABH , aBh , and of the similar parallelograms AC , ac , we have P D H B AH ah : AB : ab :: BC : bc . : But since the bases are similar , we have base BCD hence , a base bcd : BC2 : bc ( Book IV . Prop . XXV . ) ; base ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
14 other sections not shown
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex