Elements of Geometry and Trigonometry |
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Page 52
... whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be expressed in whole ...
... whole arc AB will be to the whole arc DE , as 7 is to 4. But the same reasoning would evidently apply , if in place of 7 and 4 any numbers whatever were employed ; hence , if the ratio of the angles ACB , DCE , can be expressed in whole ...
Page 121
... whole circles ; which again are as the squares of their radii ; therefore sect . ACB sect . DOE :: AC2 : DO2 ... whole circle as the arc AMB is to the whole circumference ABD ( Book III . Prop . XVII . Sch . 2. ) , or as AMBAC is to ...
... whole circles ; which again are as the squares of their radii ; therefore sect . ACB sect . DOE :: AC2 : DO2 ... whole circle as the arc AMB is to the whole circumference ABD ( Book III . Prop . XVII . Sch . 2. ) , or as AMBAC is to ...
Page 200
... whole surface of the sphere is equal to eight tri - rectangular triangles ( Prop . XVI . Cor . 3. ) ; hence , if the area of one such triangle is represented by T , the surface of the whole sphere will be expressed by 8T . This granted ...
... whole surface of the sphere is equal to eight tri - rectangular triangles ( Prop . XVI . Cor . 3. ) ; hence , if the area of one such triangle is represented by T , the surface of the whole sphere will be expressed by 8T . This granted ...
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