A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of the Nature and Use of Logarithms. Being the Second Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges ...Howe & Deforest, 1815 - 126 σελίδες |
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Σελίδα 40
... extended till it meets a line drawn from the centre through the other end . Thus AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
... extended till it meets a line drawn from the centre through the other end . Thus AD ( Fig . 3. ) is the tangent of the ... extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines ...
Σελίδα 45
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
... extend these tables beyond 90 ° ; because the sines , tangents , and secants , are of the same magnitude , in one of the quadrants of a circle , as in the others . Thus the sine of 30 ° is equal to that of 150 ° . ( Art . 90. ) 99. And ...
Σελίδα 46
... extend from the centre , to a point without the circle . 102. The numbers in the tables here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
... extend from the centre , to a point without the circle . 102. The numbers in the tables here spoken of , are called natural sines , tangents , & c . They express the lengths of the several lines which have been defined in arts . 82 , 83 ...
Σελίδα 68
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB , set off AD equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum of ...
... Extend CA to G , making AG equal to AB ; then CG is the sum of the two sides AB and AC . On AB , set off AD equal to AC ; then BD is the difference of the sides AB and AC . The sum of the two angles ACB and ABC , is equal to the sum of ...
Σελίδα 69
... extend BA to H. Then by Euc . 35 , 3 , AB × AH = AL × AD And converting the equation into a proportion , But AD ABAD :: AL : AH CD + CA = CB + CA And AL CL - CA - CB - CA - And AH = HP - PA = BP - PA ( Euc . 3. 3. ) If then , for the ...
... extend BA to H. Then by Euc . 35 , 3 , AB × AH = AL × AD And converting the equation into a proportion , But AD ABAD :: AL : AH CD + CA = CB + CA And AL CL - CA - CB - CA - And AH = HP - PA = BP - PA ( Euc . 3. 3. ) If then , for the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
acute angle added angle ACB arithmetical complement arithmetical progression b+sin base calculation centre circle cosecant Cosine Cotangent Tangent decimal degrees and minutes divided division divisor equal to radius equation errour exponents extend find the angles find the logarithm fraction geometrical progression given angle given number given side Given the angle gles greater half the sum hypothenuse JEREMIAH DAY length less line of chords line of numbers lines of sines loga logarithmic sine logarithmic TANGENT metical Mult multiplied natural number natural sines number of degrees opposite angles perpendicular positive proportion quadrant quotient radix right angled triangle rithms root secant similar triangles sine of 30 sines and cosines slider square subtracting tables tabular radius tabular sine tangent of half theorem transverse distance triangle ABC trigonometrical tables Trigonometry versed sine vulgar fraction
Δημοφιλή αποσπάσματα
Σελίδα 68 - 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.
Σελίδα 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Σελίδα 105 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Σελίδα 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Σελίδα 39 - With these the learner should make himself perfectly familiar. 82. The SINE of an arc is a straight line drawn from one end of the arc, perpendicular to a diameter which passes through the other end. Thus BG (Fig.
Σελίδα 116 - 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. By Theorem II. we have a : b : : sin. A : sin. B.
Σελίδα 37 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &c., marked with the characters °, ', ", '", &c. Thus, 32° 24...
Σελίδα 72 - ... angle. The third angle is found by subtracting the sum of the other two from 180° ; and the third side is found as in Case I.