## A Course of Mathematics ...: Composed for the Use of the Royal Military Academy ... |

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Page 110

For, from the point 1 draw any line reh to cut the curve in two points E and H; from

which let fall the

AG. GB :: de' : GH', and by sim. triangles, ID* : 16* :: De" : GH"; theref. by equality,

...

For, from the point 1 draw any line reh to cut the curve in two points E and H; from

which let fall the

**perps**. ED, Hc; and bisect DG in K. Then, by theor. 1, AD. DB :AG. GB :: de' : GH', and by sim. triangles, ID* : 16* :: De" : GH"; theref. by equality,

...

Page 114

For, set A be the vertex of the curve, or extremity of the semi-transverse axis ac,

definition 19. Also, draw HEDeh parallel to Ll, Then, by theor. 2. cA* : AL” :: cD' –

cA*: ...

For, set A be the vertex of the curve, or extremity of the semi-transverse axis ac,

**perp**. to which draw AL or Al, which will be equal to the semi-conjugate, bydefinition 19. Also, draw HEDeh parallel to Ll, Then, by theor. 2. cA* : AL” :: cD' –

cA*: ...

Page 154

Or, having drawn PQ

AH is the range. For, by the last corollary, A P : A G : : A G : 4GH ; and, by similar

triangles, AP : AG : : AQ : GH, Or - - - AP : A G :: 4AQ : 4 GH 3 therefore AG = 4AQ;

...

Or, having drawn PQ

**perp**. to AG, take AG = 4AQ, and draw GH**perp**. to AH; thenAH is the range. For, by the last corollary, A P : A G : : A G : 4GH ; and, by similar

triangles, AP : AG : : AQ : GH, Or - - - AP : A G :: 4AQ : 4 GH 3 therefore AG = 4AQ;

...

Page 157

Draw Po

inclined plane in Ki take AE = 4AK, draw EF parallel to AG, and FI parallel to AP

or DQ ; so shall AI be the range on the oblique plane. For AH = 4AD, therefore eH

is ...

Draw Po

**perp**. to AG, and Qp**perp**. to the horizontal plane AF, meeting theinclined plane in Ki take AE = 4AK, draw EF parallel to AG, and FI parallel to AP

or DQ ; so shall AI be the range on the oblique plane. For AH = 4AD, therefore eH

is ...

Page 158

If there be given the range A1 and the velocity, or the impetus, the direction will

hence be easily found thus: Take Ak = A1, draw kg

described with the radius Ae in two points q and q; then Aq or Aq will be the ...

If there be given the range A1 and the velocity, or the impetus, the direction will

hence be easily found thus: Take Ak = A1, draw kg

**perp**. to AH, meeting the circledescribed with the radius Ae in two points q and q; then Aq or Aq will be the ...

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### Popular passages

Page 66 - 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.

Page 3 - 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.

Page 173 - Half the Length of the Pendulum, as the Circumference of a Circle is to its Diameter...

Page 229 - Hence the magnitude of the whole body, is to the magnitude of the part immersed, as the specific gravity of the fluid, is to that of the body.

Page 15 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.

Page 90 - GLAZIERS' WORK. — Glaziers take their dimensions either in feet, inches, and parts ; or feet, tenths, and hundredths. And they compute their work in square feet. In taking the length and breadth of a window, the cross bars between the squares are included. Also, windows of round or oval forms are measured as square, measuring them to their greatest length and breadth, on account of the waste in cutting the glass.

Page 46 - Ex. 2. To find the whole surface of a triangular prism, whose length is 20 feet, and each side of its end or base 18 inches.

Page 13 - DF; that is, as the sum of the sides is to the difference of the sides, so is the tangent of half the sum of the opposite angles, to the tangent of half their difference.

Page 24 - A ladder 40 feet long may be so placed that it shall reach a window 33 feet from the ground on one side of the street, and by turning it over, without moving the foot out of its place, it will do the same by a window 21 feet high on the other side. Required the breadth of the street.

Page 89 - Required the quantity of plastering in a room, the length being 14 feet 5 inches, breadth 13 feet 2 inches, and height 9 feet 3 inches to the under side of the cornice, which girts...