Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 226
... sine of an arc is a perpendicular let fall from one of its extremities upon a diameter passing through the other . 3. The versed sine of an arc is that portion of a diame- ter intercepted between its sine and the circumference . 4. The ...
... sine of an arc is a perpendicular let fall from one of its extremities upon a diameter passing through the other . 3. The versed sine of an arc is that portion of a diame- ter intercepted between its sine and the circumference . 4. The ...
Seite 227
... sine AD , the coversed sine CG , and the sup- plementary versed sine FD ; the tangent of AB is AH , and its co- tangent CI ; and the secant of the same arc is OH , and its cosecant OI . F B H E Several obvious consequences flow from ...
... sine AD , the coversed sine CG , and the sup- plementary versed sine FD ; the tangent of AB is AH , and its co- tangent CI ; and the secant of the same arc is OH , and its cosecant OI . F B H E Several obvious consequences flow from ...
Seite 228
... sine and the diameter ; for AB2 = AD.AF. 7. The triangles OAH and ICO being similar , AH : OA :: OC : CI ; and hence the radius is a mean proportional between the tangent of an arc and its cotangent . 8. Since ODBG = CG.CE , it follows ...
... sine and the diameter ; for AB2 = AD.AF. 7. The triangles OAH and ICO being similar , AH : OA :: OC : CI ; and hence the radius is a mean proportional between the tangent of an arc and its cotangent . 8. Since ODBG = CG.CE , it follows ...
Seite 229
... sine of the arc AB is equal to the sine of its supple- ment ABb . But B'E and b'e , or the sines of ABFʊ ' and ABFO'B ' which lie on the opposite side of the diameter , are likewise equal to BE ; that is , the inverted sine of an arc is ...
... sine of the arc AB is equal to the sine of its supple- ment ABb . But B'E and b'e , or the sines of ABFʊ ' and ABFO'B ' which lie on the opposite side of the diameter , are likewise equal to BE ; that is , the inverted sine of an arc is ...
Seite 230
... sine again contracts , and the tangent , re - appearing on the same side , shrinks also by degrees to a point . In ... sine of an arc a is equal to the sine of the arc ( 2m - 1 ) 180 ° —ɑ , and to opposite sines of ( 2m - 1 ) 180 ° + a ...
... sine again contracts , and the tangent , re - appearing on the same side , shrinks also by degrees to a point . In ... sine of an arc a is equal to the sine of the arc ( 2m - 1 ) 180 ° —ɑ , and to opposite sines of ( 2m - 1 ) 180 ° + a ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
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ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore