Plane and Solid Geometry |
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Page 2
... faces , and of all figures that are not represented on a plane . 13. A Theorem is a truth requiring demonstration . 14. A Problem is a question proposed for solution . 15. A Postulate assumes the possibility of the solution of some ...
... faces , and of all figures that are not represented on a plane . 13. A Theorem is a truth requiring demonstration . 14. A Problem is a question proposed for solution . 15. A Postulate assumes the possibility of the solution of some ...
Page 138
... face type show the approximation . 310. SCHOLIUM . By the aid of simpler methods the value of has been computed to more than eight hundred places of decimals . The first twenty figures of the result are log π = 1 π = π = = 3.14159 26535 ...
... face type show the approximation . 310. SCHOLIUM . By the aid of simpler methods the value of has been computed to more than eight hundred places of decimals . The first twenty figures of the result are log π = 1 π = π = = 3.14159 26535 ...
Page 155
... Faces . Thus in the diedral angle formed by the planes BD and BF , BE is the edge and BD and BF are the faces . A B CG K D E F 358. A diedral angle may be designated by H two letters on its edge ; or , if several diedral angles have a ...
... Faces . Thus in the diedral angle formed by the planes BD and BF , BE is the edge and BD and BF are the faces . A B CG K D E F 358. A diedral angle may be designated by H two letters on its edge ; or , if several diedral angles have a ...
Page 156
... faces may be made to coincide . 361. The magnitude of a diedral angle depends solely on the amount of divergence of its faces , and is entirely independent of their extent . 362. Two diedral angles are adjacent when they have a common ...
... faces may be made to coincide . 361. The magnitude of a diedral angle depends solely on the amount of divergence of its faces , and is entirely independent of their extent . 362. Two diedral angles are adjacent when they have a common ...
Page 157
... faces of one are prolongations of the faces of the other . 367. Diedral angles are acute , obtuse , complementary , supple- mentary , under the same conditions that hold for plane angles . 368. The demonstrations of many properties of ...
... faces of one are prolongations of the faces of the other . 367. Diedral angles are acute , obtuse , complementary , supple- mentary , under the same conditions that hold for plane angles . 368. The demonstrations of many properties of ...
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Common terms and phrases
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Popular passages
Page 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 108 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Page 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Page 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Page 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.