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 M N m m X ( M + M ) since m m quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will Let then will and For , or , and also be proportional . MN : P : Q , M2 : N2 : P2 ...
... Consequently , the four M N m m X ( M + M ) since m m quan- PROPOSITION XII . THEOREM . If four quantities are proportional , their squares or cubes will Let then will and For , or , and also be proportional . MN : P : Q , M2 : N2 : P2 ...
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 , 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 , 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 VII centre chord circ circumference circumscribed common cone convex surface Cosine 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 logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex