The Elements of Euclid |
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Page iii
... SPHERICAL TRIGONOMETRY . PHILADELPHIA : PUBLISHED BY JOHNSON AND WARNER , AND SOLD AT THEIR BOOKSTORES IN PHILADELPHIA , RICHMOND , ( Vir . ) AND LEXINGTON , ( Ken . ) The UNIVERSITY OF CHICAGO LIBRARY @ A457 PREFACE . THE 1811 . THE ...
... SPHERICAL TRIGONOMETRY . PHILADELPHIA : PUBLISHED BY JOHNSON AND WARNER , AND SOLD AT THEIR BOOKSTORES IN PHILADELPHIA , RICHMOND , ( Vir . ) AND LEXINGTON , ( Ken . ) The UNIVERSITY OF CHICAGO LIBRARY @ A457 PREFACE . THE 1811 . THE ...
Page viii
... friendly assistance of a learned gen- tleman . To which are also added , the Elements of Plane and Spherical Trigonometry , which are commonly taught after the Elements of Euclid . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. viii ...
... friendly assistance of a learned gen- tleman . To which are also added , the Elements of Plane and Spherical Trigonometry , which are commonly taught after the Elements of Euclid . THE ELEMENTS OF EUCLID . BOOK I. DEFINITIONS . I. viii ...
Page 197
... sphere is a solid figure described by the revolution of a semicircle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the semicircle revolves . XVI . The centre of a sphere is ...
... sphere is a solid figure described by the revolution of a semicircle about its diameter , which remains unmoved . XV . The axis of a sphere is the fixed straight line about which the semicircle revolves . XVI . The centre of a sphere is ...
Page 286
... sphere . Let the spheres be cut by a plane passing through the centre ;. the common sections of it with the spheres shall be circles ; because the sphere is described by the revolution of a semi- circle about the diameter remaining ...
... sphere . Let the spheres be cut by a plane passing through the centre ;. the common sections of it with the spheres shall be circles ; because the sphere is described by the revolution of a semi- circle about the diameter remaining ...
Page 288
... like be done also in the other three qua- drants , and in the other hemisphere ; there shall be for- med a solid polyhedron described in the sphere , compo- sed of pyramids , the bases of which are the. 288 THE ELEMENTS.
... like be done also in the other three qua- drants , and in the other hemisphere ; there shall be for- med a solid polyhedron described in the sphere , compo- sed of pyramids , the bases of which are the. 288 THE ELEMENTS.
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore