## A Treatise on Mensuration, Both in Theory and Practice |

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Page 116

o ) у sine of

the series will become ** + * + cofine US + fine of

angle CAP ( 70 ° ) in the nonagon . If n = 11 , there will come out the equation ...

o ) у sine of

**double**the complement of the CAP ( 647 ) in the heptagon . If n = 9 ,the series will become ** + * + cofine US + fine of

**double**the complement of theangle CAP ( 70 ° ) in the nonagon . If n = 11 , there will come out the equation ...

Page 120

... and that the tangent of any are being given , the tangent of

easily be had ; if there be affuned foine small simple number for the tangent of an

are , and then the tangent of the

... and that the tangent of any are being given , the tangent of

**double**that arc caneasily be had ; if there be affuned foine small simple number for the tangent of an

are , and then the tangent of the

**double**arc be continually taken , until a tangent ... Page 295

And .67357436 X 25 X 35 = 589.377565 = the greater segment . PROBL EM VII .

To find the Area of an Elliptic Segment cut off by a

Dianeter ; that is , by a Line Oblique to the Axes . Divide the absciss AF ( fig . to

prob .

And .67357436 X 25 X 35 = 589.377565 = the greater segment . PROBL EM VII .

To find the Area of an Elliptic Segment cut off by a

**Double**Ordinate to anyDianeter ; that is , by a Line Oblique to the Axes . Divide the absciss AF ( fig . to

prob .

Page 358

To find the Length of the Curve or Arc of a Parabola , cut of by a

to the Axe . R U L E 1. * Divide the

quotient q . Add DEMONSTRATION . Putting z = any curve beginning at the ...

To find the Length of the Curve or Arc of a Parabola , cut of by a

**Double**Ordinateto the Axe . R U L E 1. * Divide the

**double**ordinate by the parameter , and call thequotient q . Add DEMONSTRATION . Putting z = any curve beginning at the ...

Page 361

Therefore 9 X 1.4263785 = 12.8374065 is the length of the curve required .

R U L E II . * Putting y to denote the ordinate , and q the quotient arising from the

divilion of the

.69 ...

Therefore 9 X 1.4263785 = 12.8374065 is the length of the curve required .

R U L E II . * Putting y to denote the ordinate , and q the quotient arising from the

divilion of the

**double**ordinate by * DEMONSTRATION . 2 3 ? 306 - 2 a2 2.4 at 2.4.69 ...

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### Common terms and phrases

abſciſs alſo altitude angle baſe become breadth called caſk circle circumference common cone conjugate conſequently Corol corollary curve DEMONSTRATION deſcribe diameter difference diſtance divided double draw drawn ellipſe equal evident EXAMPLE feet fides figure firſt fixed folidity fruſtum gallons give given greater half height hence hyperbola inches laſt length leſs mean meaſure method middle multiply muſt nearly Note oppoſite ordinate parabola parallel perpendicular places plane prob PROBLEM proportional putting quantity quotient radius remainder root rule ſaid ſame ſection ſegment ſeries ſet ſhall ſide ſimilar ſolid ſphere ſpheroid ſpindle ſquare ſtation ſum ſuppoſing ſurface taken tangent theſe thoſe triangle uſed verſed whole whoſe yards zone

### Popular passages

Page 535 - ... being entirely dependent on them, and therefore they should be taken of as great length as possible ; and it is best for them to run along some of the hedges or boundaries of one or more fields, or to pass through some of their angles. All things being determined for these stations, you must take more inner stations, and continue to divide and subdivide, till at last you come to single fields ; repeating the same work for the inner stations as for the outer ones, till the whole is finished.

Page 91 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.

Page 2 - A Right Angle is that which is made by one line perpendicular to another. Or when the angles on each side are equal to one another, they are right angles.

Page 614 - ... for the double row of slates at the bottom, or for how much one row of slates or tiles is laid over another. When the roof is of a true pitch, that is, forming a right angle at top ; then the breadth of the building, with its half added, is the girt over both sides nearly.

Page 617 - The length of a room being 20 feet, its breadth 14 feet 6 inches, and height 10 feet 4 inches ; how many yards of painting are in it, deducting a...

Page 6 - A quadrant, or quarter of a circle, is a sector, having a quarter of the circumference for its arc, and the two radii are perpendicular to each other, as G.

Page 608 - Chimneys are commonly measured as if they were solid, deducting only the vacuity from the hearth to the mantle, on account of the trouble of them. All windows, doors, &c, are to be deducted out of the contents of the walls in which they are placed.

Page 62 - From the edge of a ditch 18 feet wide, surrounding a fort, I took the angle of elevation of the top of the wall and found it 62° 40...

Page 7 - The Measure of an angle, 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 461 - Ans. the upper part 13'867. the middle part 3 '605. the lower part 2-528. QUEST. 48. A gentleman has a bowling green, 300 feet long, and 200 feet broad, which he would raise 1 foot higher, by means of the earth to be dug out of a ditch that goes round it : to what depth must the ditch be dug, supposing its breadth to be every where 8 feet i Ans. 7f-| feet. QUEST. 49. How high above the earth must a person be raised, that he may see j. of its surface ? Ans. to the height of the earth's diameter.