Elements of Plane and Solid GeometryGinn, Heath, 1877 - 398 σελίδες |
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Σελίδα 9
... angle , consequently , will not be changed .. 24. DEF . Adjacent Angles are angles having a common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D Α C B -F 25. DEF . A Right Angle is an angle ...
... angle , consequently , will not be changed .. 24. DEF . Adjacent Angles are angles having a common vertex and a common side between them . Thus the angles CDE and CDF are adjacent angles . E D Α C B -F 25. DEF . A Right Angle is an angle ...
Σελίδα 10
... right angles and the given angle . Thus ACD is the supplement of the angle D C B ; also D C B is the supplement of the angle A C D. 32. DEF . Vertical Angles are angles which have the same vertex , and their sides extending in opposite ...
... right angles and the given angle . Thus ACD is the supplement of the angle D C B ; also D C B is the supplement of the angle A C D. 32. DEF . Vertical Angles are angles which have the same vertex , and their sides extending in opposite ...
Σελίδα 11
... right angles ; and the sum of all the angles about a point on one side of a straight line drawn through that point , as AOB BOC + COD , etc. , Fig . 2 , is equal to two right angles . Hence two adjacent angles , O CA and OC B , formed ...
... right angles ; and the sum of all the angles about a point on one side of a straight line drawn through that point , as AOB BOC + COD , etc. , Fig . 2 , is equal to two right angles . Hence two adjacent angles , O CA and OC B , formed ...
Σελίδα 14
... right angle . rt . right angles . > is ( or are ) greater than . < is ( or are ) less than . rt . A right triangle . rt . A right triangles . O circle . ― circles . increased by . diminished by . X multiplied by . divided by .. Post ...
... right angle . rt . right angles . > is ( or are ) greater than . < is ( or are ) less than . rt . A right triangle . rt . A right triangles . O circle . ― circles . increased by . diminished by . X multiplied by . divided by .. Post ...
Σελίδα 15
... angles are equal . A P Let line OP cross A B at C. B We are to prove LOCB = LACP . LOCA + Z OCB 2 rt . 4 , == $ 34 ... right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES . 15 PERPENDICULAR AND ...
... angles are equal . A P Let line OP cross A B at C. B We are to prove LOCB = LACP . LOCA + Z OCB 2 rt . 4 , == $ 34 ... right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES . 15 PERPENDICULAR AND ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC ABCD altitude apothem arcs A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 188 - 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.
Σελίδα 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 221 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 217 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα 44 - Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.
Σελίδα 186 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 346 - A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having the same altitude as the pyramid S-ABCDE, and a base A'B'C' equivalent to the base ABCDE, and in the same plane with it.
Σελίδα 95 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.