Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 225
... hypotenuse to either of the side , so the radius to the sine of the angle opposite to that side ; and as either of ... hypotenuse . For CG is the secant of Ff the angle G ( def . 7. ) , and PLANE TRIGONOMETRY . 225.
... hypotenuse to either of the side , so the radius to the sine of the angle opposite to that side ; and as either of ... hypotenuse . For CG is the secant of Ff the angle G ( def . 7. ) , and PLANE TRIGONOMETRY . 225.
Σελίδα 226
... hypotenuse be made the radius , the sides become the sines of the opposite angles ; and if one of the sides be made the radius , the other side becomes the tan- gent of the opposite angle , and the hypotenuse the secant of it . PROP ...
... hypotenuse be made the radius , the sides become the sines of the opposite angles ; and if one of the sides be made the radius , the other side becomes the tan- gent of the opposite angle , and the hypotenuse the secant of it . PROP ...
Σελίδα 234
... hypotenuse and AB . R : cos B :: CB : AB . 2 an angle . AC and C , a BC . side and one of the acute angles . AB . CosCR :: AC : BC . R : tan C :: AC : AB . 3 4 CB and BA , the hypotenuse and a side . C. AC . CB : BA :: R : sin C. R ...
... hypotenuse and AB . R : cos B :: CB : AB . 2 an angle . AC and C , a BC . side and one of the acute angles . AB . CosCR :: AC : BC . R : tan C :: AC : AB . 3 4 CB and BA , the hypotenuse and a side . C. AC . CB : BA :: R : sin C. R ...
Σελίδα 235
... hypotenuse BC and the side AB are given to find AC , this may be done either as directed in the Table , or by the 47th of the first ; for since AC = BC2 - BA , AC = BC2 - BA2 . This value of AC will be easy to calculate by loga- rithms ...
... hypotenuse BC and the side AB are given to find AC , this may be done either as directed in the Table , or by the 47th of the first ; for since AC = BC2 - BA , AC = BC2 - BA2 . This value of AC will be easy to calculate by loga- rithms ...
Σελίδα 256
... hypotenuse will be less than a quadrant ; and if they be of different affection , the hypotenuse will be greater than a quadrant . Let ABC be a right angled spherical triangle ; according as the two sides AB , AC are of the same or of ...
... hypotenuse will be less than a quadrant ; and if they be of different affection , the hypotenuse will be greater than a quadrant . Let ABC be a right angled spherical triangle ; according as the two sides AB , AC are of the same or of ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore