The Elements of Euclid |
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Page 482
... sine CD , and that ex- tremity , is called the Versed Sine of the arch AC , or angle ABC . 23 VI . A straight line AE touching the circle at A , one extremity of the arch AC , and meeting the diameter BC passing through the other ...
... sine CD , and that ex- tremity , is called the Versed Sine of the arch AC , or angle ABC . 23 VI . A straight line AE touching the circle at A , one extremity of the arch AC , and meeting the diameter BC passing through the other ...
Page 483
... sine , versed sine , tangent , and se . cant , of any arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any other arch which is the measure of the same angle , as the radius of ...
... sine , versed sine , tangent , and se . cant , of any arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and secant , of any other arch which is the measure of the same angle , as the radius of ...
Page 484
... sine of the angle ABC opposite to it ; and if either side BA be made ra- dius , the other side AC will be the tangent of the angle ABC opposite to it , and the hypothenuse BC the secant of the saine angle . About B as a centre , with BC ...
... sine of the angle ABC opposite to it ; and if either side BA be made ra- dius , the other side AC will be the tangent of the angle ABC opposite to it , and the hypothenuse BC the secant of the saine angle . About B as a centre , with BC ...
Page 486
... sine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC con- tained by any two sides BA , BC is to the difference of the sum of the squares of RA , BC , and the square of the base AC , as the ...
... sine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC con- tained by any two sides BA , BC is to the difference of the sum of the squares of RA , BC , and the square of the base AC , as the ...
Page 487
... sine of BAD , which is the complement of the angle ABC , that is , as radius to the co - sine of ABC . PROP . VI . FIG . 11 : IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half the ...
... sine of BAD , which is the complement of the angle ABC , that is , as radius to the co - sine of ABC . PROP . VI . FIG . 11 : IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by half the ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore