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. 1867 Excerpt: ...XT. DEFINITIONS. 1. A Solid is that which has length, breadth, and thickness. 2. That which bounds a solid is a superficies. 3. A straight line is perpendicular, or at right angles, to a plane, when it makes right angles with every straight line meeting it in that plane. 4. A plane is perpendicular to a plane, when the ...
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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. 1867 Excerpt: ...XT. DEFINITIONS. 1. A Solid is that which has length, breadth, and thickness. 2. That which bounds a solid is a superficies. 3. A straight line is perpendicular, or at right angles, to a plane, when it makes right angles with every straight line meeting it in that plane. 4. A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. 5. The inclination of a straight line to a plane is the acute angle contained by that straight line, and another drawn from the point at which the first line meets the plane to the point at which a perpendicular to the plane drawn from any point of the first line above the plane, meets the same plane. 6. The inclination of a plane to a plane is the acute angle contained by two straight lines drawn from any the same point of their common section at right angles to it, one in one plane, and the other in the other plane. 7. Two planes are said to have the same or a like inclination to one another, which two other planes have, when the said angles of inclination are equal to one another. 8. Parallel planes are such as do not meet one another though produced. 9. A solid angle is that which is made by more than two plane angles, which are not in the same plane, meeting at one point. 10. Equal and similar solid figures are such as are contained by similar planes equal in number and magnitude. See the Notes. 11. Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the samo number of similar planes. 12. A pyramid is a solid figure contained by planes which are constructed between one plane and one point above it at which they meet. 13. A prism is a solid figure contain...
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All Editions of The Elements of Euclid for the use of schools and colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books