Euclide's Elements; The Whole Fifteen Books Compendiously Demonstrated with Archimede's Theorems of the Sphere and Cylinder, Investigated by the Metho (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1751 edition. Excerpt: ...solid figures are such as are contained under like planes equal in number. X. Equal and like solid figures are such as are contained under like planes equal both in multitude and magnitude. XI. A solid angle is the inclination of more than two right-lines which touch one another, and are not in the fame superficies. Or thus; A solid angle is that which is contained under more than two plane angles not being in the fame superficies but consisting all at one-point. XII. A Pyramid is a solid figure comprehended under divers planes set upon one plane (which is the base of the pyramid, ) and gathered together to one point, XIII. A Prism is a solid figure contained under planes, whereof the two opposite are equal, like, and parallel; but the others are parallelograms. XIV. A Sphere is a solid figure made when the diameter os a semicircle abiding unmoved, the semicircle is turned round about, till it return to the fame place from whence it began to be moved. Cor oil Hence, all the rays drawn from the center to the superficies of a sphere, are equal amongst themselves. XV. The Axis of a sphere, is that fixed right-line, about which the semicircle is moved, XVI. The Center of a sphere, is the fame point with the center of the semicircle. XVII. The Diameter of a sphere, is a right-line drawn thro1 the center, and terminated on either fi.de in the superficies of the sphere. XVIII. A Cone is a figure made, when one fide of a rectangled triangle vi-z. one of those that contain the right angle) remaining fixed, the triangle is turned round about till it return to the-place from whence it it first moved. And if the fixed right-line be equal to the other which containeth the right-angle, then the Cone is a rectangled Cone: But if it be less, it is an..