Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 σελίδες |
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Σελίδα 232
... sinAC ' = sinAB cosBC - cosAB sinBC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A = sinA 2cosA . Cor . 3. Let the arc A contain 45 ° ; then R sin ( 459B ) = sin45 ° ( cosBsinB ) = √R2 ( cosBsinB ) or R sin ...
... sinAC ' = sinAB cosBC - cosAB sinBC . Cor . 2. If the two arcs A and B be equal , it is obvious that R sin2A = sinA 2cosA . Cor . 3. Let the arc A contain 45 ° ; then R sin ( 459B ) = sin45 ° ( cosBsinB ) = √R2 ( cosBsinB ) or R sin ...
Σελίδα 234
... ( sinAC + sinAC ' ) = 2cosBC sinAB . Cor . 1. Hence , likewise , of three equidifferent arcs , the rectangle under the radius and the difference of the sines of the extremes , is equal to twice the rectangle under the sine of the common ...
... ( sinAC + sinAC ' ) = 2cosBC sinAB . Cor . 1. Hence , likewise , of three equidifferent arcs , the rectangle under the radius and the difference of the sines of the extremes , is equal to twice the rectangle under the sine of the common ...
Σελίδα 235
... of half their differ- ence . But ( II.21.El. ) IC2 - CC2 = IC.2C'E ' , or C'K2 - CF2 = CE.C'E ' ; consequently sin2 AB - sin2 BC = sin AC sinAC ' , or , employing the general notation , sin A - sinB2 = sin ( A + B TRIGONOMETRY . 235.
... of half their differ- ence . But ( II.21.El. ) IC2 - CC2 = IC.2C'E ' , or C'K2 - CF2 = CE.C'E ' ; consequently sin2 AB - sin2 BC = sin AC sinAC ' , or , employing the general notation , sin A - sinB2 = sin ( A + B TRIGONOMETRY . 235.
Σελίδα 239
... sinAC + sinAC ' : sinAC- AC + AC sinAC ' :: tan 2 : tan AC - AC 2 Cor . 1. The sines of the sum and difference of two arcs are proportional to the sum and difference of their tangents . For CE : C'E ' : : HL , or BL + BH : HL , or BL ...
... sinAC + sinAC ' : sinAC- AC + AC sinAC ' :: tan 2 : tan AC - AC 2 Cor . 1. The sines of the sum and difference of two arcs are proportional to the sum and difference of their tangents . For CE : C'E ' : : HL , or BL + BH : HL , or BL ...
Σελίδα 368
... sinAC + sin AD = HO + sin AD = AO.tanBAO + sinAD . Wherefore , in general , sin a + sin2a + sin3a sin na = vers nq.cotza + sin na . Hence the sum of the sines in the whole semicircle is = cotła . Thus , if the sines for each degree up ...
... sinAC + sin AD = HO + sin AD = AO.tanBAO + sinAD . Wherefore , in general , sin a + sin2a + sin3a sin na = vers nq.cotza + sin na . Hence the sum of the sines in the whole semicircle is = cotła . Thus , if the sines for each degree up ...
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angle altitude angle ABC angle ADB angle BAC angle BCD 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 Geometry greater half Hence hypotenuse inscribed intercepted 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 side AC sides AB sinAC sinB sine square of AB square of AC tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Σελίδα 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Σελίδα 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.