Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical Problems |
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Page 26
... ABCD be a parallelo- gram . We are to prove that the sum of the angles A , B , C and D , is equal to four right angles , or to 360 ° . A B Because AD and BC are parallel lines , and AB inter- sects them , the two interior angles A and B ...
... ABCD be a parallelo- gram . We are to prove that the sum of the angles A , B , C and D , is equal to four right angles , or to 360 ° . A B Because AD and BC are parallel lines , and AB inter- sects them , the two interior angles A and B ...
Page 30
... ABCD be a quadrilateral ; then we are to prove that the sum of the four in- terior angles , that is A + B + C + D , is equal to four right angles . D B Draw the diagonal AC , dividing the quadrilateral into two triangles , ABC , ADC ...
... ABCD be a quadrilateral ; then we are to prove that the sum of the four in- terior angles , that is A + B + C + D , is equal to four right angles . D B Draw the diagonal AC , dividing the quadrilateral into two triangles , ABC , ADC ...
Page 39
... ABCD be a parallelogram . Then we are to show that AB = DC , AD = BC , | _ A = LC , and LADC = LABC . Draw a diagonal , as BD ; now , be- A cause AB and DC are parallel , the al- ternate angles ABD and BDC are equal , ( Th . 6 ) . For ...
... ABCD be a parallelogram . Then we are to show that AB = DC , AD = BC , | _ A = LC , and LADC = LABC . Draw a diagonal , as BD ; now , be- A cause AB and DC are parallel , the al- ternate angles ABD and BDC are equal , ( Th . 6 ) . For ...
Page 42
... ABCD and EFGH , be two parallelograms on equal bases , AB and EF , and between the same parallels , AF and DG ; then we are A B to prove that they are equal in area . E AB = EF = HG ; but lines which join equal and parallel lines , are ...
... ABCD and EFGH , be two parallelograms on equal bases , AB and EF , and between the same parallels , AF and DG ; then we are A B to prove that they are equal in area . E AB = EF = HG ; but lines which join equal and parallel lines , are ...
Page 44
... ABCD be a rect- angle , and ABEF a rhom- F D E C boid having the same base , and their opposite sides in the same line parallel to the base . B We are now to prove that the perimeter ABCDA is less than ABEFA . Because AD is a ...
... ABCD be a rect- angle , and ABEF a rhom- F D E C boid having the same base , and their opposite sides in the same line parallel to the base . B We are now to prove that the perimeter ABCDA is less than ABEFA . Because AD is a ...
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Common terms and phrases
2sin AB² ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter difference distance divided draw equal angles equation equiangular equivalent find the angle formulæ four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpendicular plane ST polyedron PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment semi-polygon similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY square straight line Tang tangent three angles three sides triangle ABC triangular prisms Trigonometry vertex vertical angle volume