Elements of Geometry and Trigonometry |
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Page 34
... the ratio of 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,
... the ratio of 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
Adrien Marie Legendre Charles Davies. In the same manner , the ratio of any other two magnitudes C and D may be expressed by Px C ' to QxC ' , P and Q being also integral numbers , and their ratio will be the same as that of P to Q. 2 ...
Adrien Marie Legendre Charles Davies. In the same manner , the ratio of any other two magnitudes C and D may be expressed by Px C ' to QxC ' , P and Q being also integral numbers , and their ratio will be the same as that of P to Q. 2 ...
Page 42
... manner , two circumferences touch each other when they have but one point in common . 9. A polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the circle is said to be ...
... manner , two circumferences touch each other when they have but one point in common . 9. A polygon is circumscribed about a circle , when all its sides are tangents to the circumference : in the same case , the circle is said to be ...
Page 56
... manner it might be proved that the angle AED is measured by half of AFD + BC . PROPOSITION XX . THEOREM . The angle formed by two secants , is measured by half the diffe- rence of the arcs included between its sides . Let AB , AC , be ...
... manner it might be proved that the angle AED is measured by half of AFD + BC . PROPOSITION XX . THEOREM . The angle formed by two secants , is measured by half the diffe- rence of the arcs included between its sides . Let AB , AC , be ...
Page 57
... manner , above or beneath the line AB , a second point E , equally distant from the points A and B ; through the two points D and E , draw the line DE : it will bisect the line AB in C. " AX Br For , the two points D and E , being each ...
... manner , above or beneath the line AB , a second point E , equally distant from the points A and B ; through the two points D and E , draw the line DE : it will bisect the line AB in C. " AX Br For , the two points D and E , being each ...
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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