A Course of Mathematics: In Three Volumes : Composed for the Use of the Royal Military Academy ...F.C. & J. Rivington, 1811 |
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Seite 6
... proportional to the cosine , sine , and radius . 2d , CF : CB :: CA : CH ; whence the secant is known , being a third proportional to the cosine and radius . 3d , BF : FC :: CD : DL ; whence the cotangent is known , being a fourth ...
... proportional to the cosine , sine , and radius . 2d , CF : CB :: CA : CH ; whence the secant is known , being a third proportional to the cosine and radius . 3d , BF : FC :: CD : DL ; whence the cotangent is known , being a fourth ...
Seite 8
... proportional , namely , AC : CF :: AD or BC DE ; that is , the side AC is to the sine of its opposite angle B , as the side BC is to the sine of its opposite angle A. Note 1. In practice , to find an angle , begin the proportion with a ...
... proportional , namely , AC : CF :: AD or BC DE ; that is , the side AC is to the sine of its opposite angle B , as the side BC is to the sine of its opposite angle A. Note 1. In practice , to find an angle , begin the proportion with a ...
Seite 13
... proportional as in this theorem . EXAMPLE I. In the plane triangle ABC , Given AB 345 yards AC 232 the sides BC 174.07 To find the angles . 1. Geometrically . Draw the base AB = 345 by a scale of equal parts . With radius 232 , and ...
... proportional as in this theorem . EXAMPLE I. In the plane triangle ABC , Given AB 345 yards AC 232 the sides BC 174.07 To find the angles . 1. Geometrically . Draw the base AB = 345 by a scale of equal parts . With radius 232 , and ...
Seite 29
... CF : A ABC :: A ABC : BG.DF , that is , the AABC is a mean proportional between CG.CF and AG . DF , or between is . ( is - AB ) and ( § S — AC ) . ( † S — BC ) . Q. E. D. Ex . 1. To find the area of the triangle Ex . I. .OF PLANES . 29.
... CF : A ABC :: A ABC : BG.DF , that is , the AABC is a mean proportional between CG.CF and AG . DF , or between is . ( is - AB ) and ( § S — AC ) . ( † S — BC ) . Q. E. D. Ex . 1. To find the area of the triangle Ex . I. .OF PLANES . 29.
Seite 38
... proportional to the length of the arc , or to the degrees contained in it . Ex . 1. To find the area of a circular sector , whose arc con- tains 18 degrees ; the diameter being 3 feet ? 1. By the 1st Rule . First , 3.1416 × 3 = 9 · 4248 ...
... proportional to the length of the arc , or to the degrees contained in it . Ex . 1. To find the area of a circular sector , whose arc con- tains 18 degrees ; the diameter being 3 feet ? 1. By the 1st Rule . First , 3.1416 × 3 = 9 · 4248 ...
Häufige Begriffe und Wortgruppen
16 feet absciss altitude axis ball base beam body breadth CA² CD² centre of gravity circle circular segment circumference column cone constant Corol Cosine Cotang cube cubic cubic foot curve cylinder DE² denote density descending diameter direction distance divided draw drawn ellipse equal equation figure find the area find the fluent fluent of EXAM fluid foot force frustum given fluxion Hence hyperbola inches inclined plane length lever logarithms measure motion moving multiply nearly ordinate parabola parallel parallelogram pendulum perpendicular pressure PROBLEM proportional PROPOSITION quantity QUEST radius ratio rectangle resistance right angles rule SCHOLIUM segment side sine solid space specific gravity square supposing surface Tang tangent theor THEOREM theref trapezium triangle variable velocity vibration weight whole yards
Beliebte Passagen
Seite 52 - 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.
Seite 1 - Geom.) is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.
Seite 79 - A diameter is any right line, as AB or DE, drawn through the centre, and terminated on each side by the curve ; and the extremities of the diameter, or its intersections with the curve, are its vertices. Hence all the diameters of a parabola are parallel to the axi?, and infinite in length.
Seite 23 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Seite 245 - May-pole, whose top was broken off" by a blast of wind, struck the ground at the distance of 15 feet from the foot of the pole ; what was the height of the whole May-pole, supposing the length of the broken piece to be 39 feet ?
Seite 250 - Then say, As the weight lost in water, Is to the whole weight> So is the specific gravity of water, To the specific gravity of the body.
Seite 263 - It is determined, we find, as a certain fraction of the length of a pendulum vibrating seconds in the latitude of London.
Seite 27 - To find the area of a parallelogram, the length being 12-25, and height 8-5. 12-25 length 8'5 breadth 6125 9800 104-125 area . Ex. 2. To find the area of a square, whose side is 35'25 chains. Ans. 124 acres, 1 rood, 1 perch.
Seite 72 - ARTIFICERS' WORK. ARTIFICERS compute the contents of their works by several different measures. As, Glazing and masonry, by the foot ; Painting, plastering, paving, &c, by the yard, of 9 square feet : Flooring, partitioning, roofing, tiling, &c, by the square of 100 - square feet : And brickwork...
Seite 72 - ... the whole length of the upper part of the hand-rail, and girt over its end till it meet the top of the...