Elements of Geometry and Trigonometry |
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Page 32
... common side BD ; and since AD , BC , are parallel , they have also the D angle ADB = DBC , ( Prop . XX . Cor . 2. ) ; and since AB , CD , are parallel , the angle ABD BDC : hence the two triangles are equal ( Prop . VI . ) ; therefore ...
... common side BD ; and since AD , BC , are parallel , they have also the D angle ADB = DBC , ( Prop . XX . Cor . 2. ) ; and since AB , CD , are parallel , the angle ABD BDC : hence the two triangles are equal ( Prop . VI . ) ; therefore ...
Page 33
... common , and the side AB = DC ; hence the tri- angle ABD is equal to the triangle DBC ( Prop . V. ) ; therefore , the side AD is equal to BC , the angle ADB = DBC , and conse- ` quently AD is parallel to BC ; hence the figure ABCD is a ...
... common , and the side AB = DC ; hence the tri- angle ABD is equal to the triangle DBC ( Prop . V. ) ; therefore , the side AD is equal to BC , the angle ADB = DBC , and conse- ` quently AD is parallel to BC ; hence the figure ABCD is a ...
Page 34
... A to B , will be the same as the ratio of M × A ' to N × A ' ; that is the same as the ratio of M to N , since ' A ' is a common unit . In the same manner , the ratio of any other 34 GEOMETRY . BOOK II Ratios and Proportions,
... A to B , will be the same as the ratio of M × A ' to N × A ' ; that is the same as the ratio of M to N , since ' A ' is a common unit . In the same manner , the ratio of any other 34 GEOMETRY . BOOK II Ratios and Proportions,
Page 35
... common multiplier being m . 10. Two quantities A and B are said to be reciprocally pro- portional , or , invasely proportional , when one of them is pro- portional to unity divided by the ether , in which case their pro- duct is always ...
... common multiplier being m . 10. Two quantities A and B are said to be reciprocally pro- portional , or , invasely proportional , when one of them is pro- portional to unity divided by the ether , in which case their pro- duct is always ...
Page 41
... common language , the circle is sometimes confounded with its circumference : but the correct expression may always be easily recurred to if we bear in mind that the circle is a surface which has length and breadth , while the ...
... common language , the circle is sometimes confounded with its circumference : but the correct expression may always be easily recurred to if we bear in mind that the circle is a surface which has length and breadth , while the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex