Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful Tables |
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Page 21
... Prop . IV . , B. VI . ) ; hence the sine of 30 ° is equal to half of the radius . ( 23. ) The versed sine of an arc is that part of the diameter intercepted between the sine and the arc . Thus GA is the versed sine of the arc AF . ( 24 ) ...
... Prop . IV . , B. VI . ) ; hence the sine of 30 ° is equal to half of the radius . ( 23. ) The versed sine of an arc is that part of the diameter intercepted between the sine and the arc . Thus GA is the versed sine of the arc AF . ( 24 ) ...
Page 37
... Prop . 27 , B. I. ) . But , since CA is equal to CE , the angle CAE is equal to the an- gle CEA ; therefore , CAE is the half sum of the angles CAB , CBA . Also , if from the greater of the two angles CAB , CBA , there be taken their ...
... Prop . 27 , B. I. ) . But , since CA is equal to CE , the angle CAE is equal to the an- gle CEA ; therefore , CAE is the half sum of the angles CAB , CBA . Also , if from the greater of the two angles CAB , CBA , there be taken their ...
Page 38
... Prop . 31 , Cor . , B. IV . ( 52 ) . In every plane triangle , three parts must be given to enable us to determine the others ; and of the given parts , one , at least , must be a side . For if the angles only are given , these might ...
... Prop . 31 , Cor . , B. IV . ( 52 ) . In every plane triangle , three parts must be given to enable us to determine the others ; and of the given parts , one , at least , must be a side . For if the angles only are given , these might ...
Page 49
... Prop . 11 , Cor . 3 , B. IV . ) ; or sin . 45 ° : R : 1 : √2 . Hence , Ꭱ sin . 45 ° = Ꭱ 2 . ✓2 The sine of 30 ° is equal to half radius ( Art . 22 ) . Also , since sin . A = √ R2 — cos . ' A , the sine of 60 ° , which is equal to ...
... Prop . 11 , Cor . 3 , B. IV . ) ; or sin . 45 ° : R : 1 : √2 . Hence , Ꭱ sin . 45 ° = Ꭱ 2 . ✓2 The sine of 30 ° is equal to half radius ( Art . 22 ) . Also , since sin . A = √ R2 — cos . ' A , the sine of 60 ° , which is equal to ...
Page 56
... Prop . 12 , B. IV . ) , AB ' + AC - 2ABXAD . BC2 Hence , AD = AB ' + AC2 - BC2 2AB C But in the right - angled triangle ACD , we have Hence , A D B R : AC :: cos . A : AD . ᎪᏟ RXAD cos . A AC or , by substituting the value of AD , AB ...
... Prop . 12 , B. IV . ) , AB ' + AC - 2ABXAD . BC2 Hence , AD = AB ' + AC2 - BC2 2AB C But in the right - angled triangle ACD , we have Hence , A D B R : AC :: cos . A : AD . ᎪᏟ RXAD cos . A AC or , by substituting the value of AD , AB ...
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Common terms and phrases
9 I I altitude angle of elevation arithm base chains circle Co-sine Co-tangent complement computed correction cosecant course and distance decimal diameter diff difference of latitude difference of longitude Dist divided equal equator fifth figure find the angles find the area find the Logarithm frustum given number given the angle height Hence horizontal plane hypothenuse inches latitude and departure length LO LO LO logarithmic sine measured meridian middle latitude miles minutes Multiply natural number nautical miles parallel parallel sailing perpendicular places plane sailing Prob Prop proportional quadrant radius Required the logarithmic right-angled spherical triangle right-angled triangle Sandy Hook secant ship sails side AC spherical triangle ABC SPHERICAL TRIGONOMETRY station subtract surface tabular number tang Tangent telescope theodolite Theorem vernier vertical Vulgar Fraction wyll yards zoids ΙΙ ΙΟ
Popular passages
Page 20 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.
Page 163 - In any spherical triangle, the sines of the sides are proportional to the sines of the opposite angles. In the case of right-angled spherical triangles, this proposition has already been demonstrated.
Page 69 - FIND the area of the sector having the same arc with the segment, by the last problem. Find also the area of the triangle, formed by the chord of the segment and the two radii of the sector.
Page 54 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 69 - TO THE NUMBER OF DEGREES IN THE ARC ; So IS THE AREA OF THE CIRCLE, TO THE AREA OF THE SECTOR.
Page 73 - To find the solidity of a pyramid. RULE. Multiply the area of the base by one third of the altitude.
Page vi - The characteristic of the logarithm of ANY NUMBER GREATER THAN UNITY, is one less than the number of integral figures in the given number.
Page 184 - If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches ; it is required to determine how much water will run over ? AHS.