Elements of Geometry and Trigonometry |
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Page 24
... consequently , AG - DF ( Prop . V. Cor . ) . But , by hypothesis AC = DF ; and therefore , AC = AG ( Ax . 1. ) . But the oblique line AC cannot be equal to AG , which lies nearer the perpendicular AB ( Prop . XV . ) ; therefore , BC and ...
... consequently , AG - DF ( Prop . V. Cor . ) . But , by hypothesis AC = DF ; and therefore , AC = AG ( Ax . 1. ) . But the oblique line AC cannot be equal to AG , which lies nearer the perpendicular AB ( Prop . XV . ) ; therefore , BC and ...
Page 32
... consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION XXVIII . THEOREM . In ...
... consequently , equal to the sum of the interior angles plus the exterior angles . Taking from each the sum of the interior angles , and there remains the exterior angles , equal to four right angles . PROPOSITION XXVIII . THEOREM . In ...
Page 40
... Consequently , the four quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will also be proportional . M2 : N2 :: P2 Q2 Let M : NP : Q , then will and For , or , and M3 N3 :: P3 : Q3 : MxQ ...
... Consequently , the four quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will also be proportional . M2 : N2 :: P2 Q2 Let M : NP : Q , then will and For , or , and M3 N3 :: P3 : Q3 : MxQ ...
Page 41
... consequently also to two segments : but the smaller one is always meant unless the contrary is expressed . An inscribed triangle is one which , like BAC , D * 6 BOOK III . 41 BOOK III The Circle and the Measurement of Angles,
... consequently also to two segments : but the smaller one is always meant unless the contrary is expressed . An inscribed triangle is one which , like BAC , D * 6 BOOK III . 41 BOOK III The Circle and the Measurement of Angles,
Page 44
... consequently , the angle ACD is equal EOG ( Book I. Prop . X. ) . Now , placing the semicircle ADB on its equal EGF , since the angles ACD , EOG , are equal , it is plain that the radius CD will fall on the radius OG , and the point D ...
... consequently , the angle ACD is equal EOG ( Book I. Prop . X. ) . Now , placing the semicircle ADB on its equal EGF , since the angles ACD , EOG , are equal , it is plain that the radius CD will fall on the radius OG , and the point D ...
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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