Elements of Plane and Solid GeometryGinn, Heath, & Company, 1885 - 398 σελίδες |
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Σελίδα 15
... prove ZOCA + Z OCB 2 rt . 4 , = § 34 . $ 34 Ax . 1 . = LOCA + ZACP 2 rt . 4 , ( being sup . - adj . ) . ..LOCA + ZOCB = ZOCA + ZACP . Take away from each of these equals the common ≤ O C A. Then = LOCB LACP . In like manner we may prove ...
... prove ZOCA + Z OCB 2 rt . 4 , = § 34 . $ 34 Ax . 1 . = LOCA + ZACP 2 rt . 4 , ( being sup . - adj . ) . ..LOCA + ZOCB = ZOCA + ZACP . Take away from each of these equals the common ≤ O C A. Then = LOCB LACP . In like manner we may prove ...
Σελίδα 17
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O ECO . Draw E F. On A B as an axis , fold over O C F until it comes into the plane of OE F. The line O C will take the direction of O E , ( since LCOF ...
... prove CO < any other line drawn from C to A B , as CF. Produce CO to E , making O ECO . Draw E F. On A B as an axis , fold over O C F until it comes into the plane of OE F. The line O C will take the direction of O E , ( since LCOF ...
Σελίδα 18
... prove = CA CO . Fold over CFA , on CF as an axis , until it comes into the plane of C F O. FA will take the direction of FO , ( since LCFA = LCFO , each being a rt . 4 ) . Point A will fall upon point 0 , ( FA FO , by hyp . ) . ... line ...
... prove = CA CO . Fold over CFA , on CF as an axis , until it comes into the plane of C F O. FA will take the direction of FO , ( since LCFA = LCFO , each being a rt . 4 ) . Point A will fall upon point 0 , ( FA FO , by hyp . ) . ... line ...
Σελίδα 21
... prove FE = FK .. Fold over C FA on CF as an axis , until it comes into the plane of C F B. The line FE will take the direction FK , ( < CFE LCF K , each being a rt . 4 ) . Then the point E must fall upon the point K ; otherwise one of ...
... prove FE = FK .. Fold over C FA on CF as an axis , until it comes into the plane of C F B. The line FE will take the direction FK , ( < CFE LCF K , each being a rt . 4 ) . Then the point E must fall upon the point K ; otherwise one of ...
Σελίδα 22
... prove O A = O B. Since PA = PB , OA = OB , $ 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . II . Draw CA and C B. We are to prove CA and C B unequal . One ...
... prove O A = O B. Since PA = PB , OA = OB , $ 53 ( two oblique lines drawn from the same point in a 1 , cutting off equal dis- tances from the foot of the 1 , are equal ) . II . Draw CA and C B. We are to prove CA and C B unequal . One ...
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AABC ABCD altitude apothem arc A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide cone of revolution 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 pass perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section S-ABC 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