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

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Page 45

In a plane triangle , As the sum of any two sides is to their difference , so is the

tangent of

difference . Then the

the ...

In a plane triangle , As the sum of any two sides is to their difference , so is the

tangent of

**half**the sum of their opposite angles , to the tangent of**half**theirdifference . Then the

**half**difference added to the**half**sum of the angles , givesthe ...

Page 46

Note also , That instead of the tangent of the

of

triangle ABC A B 345 yards Given AC 174'07 yards LA 37 20 Required the other

...

Note also , That instead of the tangent of the

**half**sum , we may use the cotangentof

**half**the given angle , which is the same thing . E XAMPLE I. A , B In the planetriangle ABC A B 345 yards Given AC 174'07 yards LA 37 20 Required the other

...

Page 49

Then

give the greater and less segment . Hence , in each of the right - angled triangles

, will be known two sides , and the angle opposite to one of them ; and ...

Then

**half**the difference being added to , and subtracted from ,**half**their sum , willgive the greater and less segment . Hence , in each of the right - angled triangles

, will be known two sides , and the angle opposite to one of them ; and ...

Page 347

Divide the square of the less axe of the ellipse by the square of the greater ;

multiply the quotient by the length of the frustum , or

then multiply the product by the difference between the square of the said

length of ...

Divide the square of the less axe of the ellipse by the square of the greater ;

multiply the quotient by the length of the frustum , or

**half**the length of the cask ;then multiply the product by the difference between the square of the said

**half**length of ...

Page 634

To abstract the foregoing particulars , that is , to collect together the contents of

the same kind , next to reduce their sums to the standard thickness of a brick and

a

To abstract the foregoing particulars , that is , to collect together the contents of

the same kind , next to reduce their sums to the standard thickness of a brick and

a

**half**, and then , having made the deductions , to collect the reduced sums , to ...### What people are saying - Write a review

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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.