Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 Seiten |
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Seite 11
... Theor . 2. ) And as radius to the tangent of the excess of this angle above 45 ° , so is the tangent of half the sum of the required angles to the tangent of half their difference * . * This theorem , though it requires two proportions ...
... Theor . 2. ) And as radius to the tangent of the excess of this angle above 45 ° , so is the tangent of half the sum of the required angles to the tangent of half their difference * . * This theorem , though it requires two proportions ...
Seite 12
... ( Theor . I. ) other As sine A : BC :: sine C : 5 and one leg leg AB BC AB ( by Theor . III . ) Or , as radius tang . C : AB ( by Theor . II . ) BC : The two The angles As AB BC : : radius : 6 legs AB and BC The hyp . The two 7 legs AB ...
... ( Theor . I. ) other As sine A : BC :: sine C : 5 and one leg leg AB BC AB ( by Theor . III . ) Or , as radius tang . C : AB ( by Theor . II . ) BC : The two The angles As AB BC : : radius : 6 legs AB and BC The hyp . The two 7 legs AB ...
Seite 13
... Theor . III . ) AB BC Two sides The other As AB : sin . C :: BC : sin . A AB , BC and anglesA and | ( by Theor . III . ) which added 2 an ang . CABC op . to one of them Two sides The AB , BC , and side AC 3 an opp . an- gle C Two sides ...
... Theor . III . ) AB BC Two sides The other As AB : sin . C :: BC : sin . A AB , BC and anglesA and | ( by Theor . III . ) which added 2 an ang . CABC op . to one of them Two sides The AB , BC , and side AC 3 an opp . an- gle C Two sides ...
Seite 19
... Theor . I. p . 17. ) we shall have sine O ' = sine 2 ' . 2C x sine 1 ' 2C x sine 2 ' sine 1 ' = sine 3 ' . 2C x sine 3 ' ---- sine 2'sine 4 ' . 2C x sine 4 ' - - sine 3 ′ = sine 5 ' . And thus are the sines of 6 ' , 7 ' , 8 ' , & c ...
... Theor . I. p . 17. ) we shall have sine O ' = sine 2 ' . 2C x sine 1 ' 2C x sine 2 ' sine 1 ' = sine 3 ' . 2C x sine 3 ' ---- sine 2'sine 4 ' . 2C x sine 4 ' - - sine 3 ′ = sine 5 ' . And thus are the sines of 6 ' , 7 ' , 8 ' , & c ...
Seite 21
... Theor . 1. p . 17 ) , and that to any assigned degree of exactness . The sines of all the terms of the progression 45 ' , 1 ° 30 ' , 2 ° 15 ' , & c . up to 60 ° , being thus derived , the next thing is to find , by the help of these ...
... Theor . 1. p . 17 ) , and that to any assigned degree of exactness . The sines of all the terms of the progression 45 ' , 1 ° 30 ' , 2 ° 15 ' , & c . up to 60 ° , being thus derived , the next thing is to find , by the help of these ...
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Häufige Begriffe und Wortgruppen
ABDP AC by Theor adjacent angle arch bisecting chord circle passing co-sine AC co-tangent of half common logarithm common section Comp describe the circle E. D. COROLLARY E. D. PROP equal to half extremes gent given angle given circle given point half the difference half the sum half the vertical Hence hyperbolic logarithm hypothenuse inclination intersect leg BC line of measures original circle parallel perpendicular plane of projection plane triangle ABC primitive PROB produced projected circle projected pole projecting point radius rectangle right line right-angled spherical triangle SCHOLIUM secant semi-tangents sides similar triangles sine 59 sine AC sine of half sphere spherical angle SPHERICAL PROJECTIONS spherical triangle ABC sum or difference tangent of half THEOREM THOMAS SIMPSON triangle ABC fig versed sine vertical angle whence
Beliebte Passagen
Seite 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Seite 79 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...
Seite 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Seite 28 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.
Seite 7 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those...
Seite 28 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.