Elements of Geometry and Trigonometry |
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Page 69
... reason , we have DC = AB , and FE AB ; hence DC - FE : hence , if DC and FE be taken away from the same line DE , the remainders CE and DF will be equal : hence it follows that the triangles DAF , CBE , are mutually eqilateral , and ...
... reason , we have DC = AB , and FE AB ; hence DC - FE : hence , if DC and FE be taken away from the same line DE , the remainders CE and DF will be equal : hence it follows that the triangles DAF , CBE , are mutually eqilateral , and ...
Page 78
... reason : therefore the triangles ABF , HBC , have two sides and the in- cluded angle in each equal ; therefore they are themselves equal ( Book I. Prop . V. ) . The triangle ABF is half of the rectangle BE , because they have the same ...
... reason : therefore the triangles ABF , HBC , have two sides and the in- cluded angle in each equal ; therefore they are themselves equal ( Book I. Prop . V. ) . The triangle ABF is half of the rectangle BE , because they have the same ...
Page 79
... reason of the common altitude BF , the square BCGF is to the rectangle BDEF as the base BC is . to the base BD ; therefore we have BC2 AB2 : : BC :: .. BD . Hence the square of the hypothenuse is to the square of one of the sides about ...
... reason of the common altitude BF , the square BCGF is to the rectangle BDEF as the base BC is . to the base BD ; therefore we have BC2 AB2 : : BC :: .. BD . Hence the square of the hypothenuse is to the square of one of the sides about ...
Page 82
... reason of the common ratio OE : OF , those two proportions give AE CF B :: EG FH . It may be proved in the G E A F same manner , that EG : FH :: GB : HD , and so on ; hence the lines AB , CD , are cut proportionally by the parallels AC ...
... reason of the common ratio OE : OF , those two proportions give AE CF B :: EG FH . It may be proved in the G E A F same manner , that EG : FH :: GB : HD , and so on ; hence the lines AB , CD , are cut proportionally by the parallels AC ...
Page 86
... reason is , that all figures may be divided into triangles , and any triangle into two right angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two ...
... reason is , that all figures may be divided into triangles , and any triangle into two right angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex