The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 461
... radius is to the cosine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC contained by any two sides BA , BC , is to the difference of the sum of the squares of BA , BC , and the square of ...
... radius is to the cosine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle ABC contained by any two sides BA , BC , is to the difference of the sum of the squares of BA , BC , and the square of ...
Page 462
... radius is to the square of the tangent of the angle DAG , that is , the half of BAC : but HA is half the perime- ter of the triangle ABC , and AD is the excess of the same above HD , that is , above the base BC ; but BF or CL is the ...
... radius is to the square of the tangent of the angle DAG , that is , the half of BAC : but HA is half the perime- ter of the triangle ABC , and AD is the excess of the same above HD , that is , above the base BC ; but BF or CL is the ...
Page 464
... Radius ; T. for Tangent ; and S. for Sine . Degrees , ' minutes , seconds , & c . are written in this manner ; 30 ° 25 ′ 13 ′′ , & c . which signifies 30 degrees , 25 minutes , 13 seconds , & c . Solution of the Cases of Right Angled ...
... Radius ; T. for Tangent ; and S. for Sine . Degrees , ' minutes , seconds , & c . are written in this manner ; 30 ° 25 ′ 13 ′′ , & c . which signifies 30 degrees , 25 minutes , 13 seconds , & c . Solution of the Cases of Right Angled ...
Page 469
... radius , which is supposed unity ; and is conceived to be divided into 10000000 or more decimal parts . And so the sine , tangent , or secant of an arc , may be had by the help of this table ; and , contrariwise , a sine , tangent , or ...
... radius , which is supposed unity ; and is conceived to be divided into 10000000 or more decimal parts . And so the sine , tangent , or secant of an arc , may be had by the help of this table ; and , contrariwise , a sine , tangent , or ...
Page 470
... radius CD , being given , to find the cosine DF.30 Fig . 29 . The radius CD , and the sine DE , being given in the right angled triangle CDE , there will be given ( by the last Prop . ) ✓ CDq — DEq = ( CE = ) DF . PROP . III . PROB ...
... radius CD , being given , to find the cosine DF.30 Fig . 29 . The radius CD , and the sine DE , being given in the right angled triangle CDE , there will be given ( by the last Prop . ) ✓ CDq — DEq = ( CE = ) DF . PROP . III . PROB ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore