A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and BonnycastleF. Nichols, 1811 - 128 σελίδες |
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Αποτελέσματα 1 - 5 από τα 48.
Σελίδα 1
... arc on which it stands is to the whole cir . cumference of the circle . Let ABC be an angle at the centre of the circle ACF , standing on the arc AC ; the angle ABC : four right an- gles :: arc AC : whole circumference ACF . D H K B G F ...
... arc on which it stands is to the whole cir . cumference of the circle . Let ABC be an angle at the centre of the circle ACF , standing on the arc AC ; the angle ABC : four right an- gles :: arc AC : whole circumference ACF . D H K B G F ...
Σελίδα 2
... angle ABC , the same number of parts will be contained in the arc GH of the other circle , subtending the same angle ABC . 5. COR . 4. Hence , if a circle of any radius whatever be di- vided into 360 equal parts , called degrees , each ...
... angle ABC , the same number of parts will be contained in the arc GH of the other circle , subtending the same angle ABC . 5. COR . 4. Hence , if a circle of any radius whatever be di- vided into 360 equal parts , called degrees , each ...
Σελίδα 3
... angles :: the arc AC circumfe- rence ADEFA ( 1. ) , therefore the angle ABC = ACX4 right angles . But four right angles are a constant circum . ADEFA quantity , and the circumferences of circles are as their diame- ters or radii ( 8. 1 ...
... angles :: the arc AC circumfe- rence ADEFA ( 1. ) , therefore the angle ABC = ACX4 right angles . But four right angles are a constant circum . ADEFA quantity , and the circumferences of circles are as their diame- ters or radii ( 8. 1 ...
Σελίδα 5
... degrees ( 6 ) . Draw tAT touching the circle in A ; and draw the radius CB , and produce it till it meet the line tAT in T. . 13. DEF . 1. The difference of any arc from a quadrant , or of any angle from 90 degrees , is called the ...
... degrees ( 6 ) . Draw tAT touching the circle in A ; and draw the radius CB , and produce it till it meet the line tAT in T. . 13. DEF . 1. The difference of any arc from a quadrant , or of any angle from 90 degrees , is called the ...
Σελίδα 6
... angle which is measured by that arc . 17. DEF . 5. The versed sine of an arc is that part of the diameter passing through ... an arc is a straight line touch- ing the circle in the beginning of the arc , produced thence till it meets the ...
... angle which is measured by that arc . 17. DEF . 5. The versed sine of an arc is that part of the diameter passing through ... an arc is a straight line touch- ing the circle in the beginning of the arc , produced thence till it meets the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sine² sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Δημοφιλή αποσπάσματα
Σελίδα 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα ix - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Σελίδα 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Σελίδα 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Σελίδα 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.