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

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Page 45

In a plane triangle , As the

tangent of half the

difference . Then the half difference added to the half

the ...

In a plane triangle , As the

**sum**of any two sides is to their difference , so is thetangent 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

When , in this case , the triangle is rightangled , the longest side will be found by

extracting the square root of the

then the angles will be found by the first problem . Note also , That instead of the

...

When , in this case , the triangle is rightangled , the longest side will be found by

extracting the square root of the

**sum**of the squares of the other two sides ; andthen the angles will be found by the first problem . Note also , That instead of the

...

Page 49

or base , dividing it into two fegments , and the whole triangle into two right -

angled triangles ; it will be As the base , or

the other two sides :: So is the difference of those sides : To the difference of the ...

or base , dividing it into two fegments , and the whole triangle into two right -

angled triangles ; it will be As the base , or

**sum**of the segments : Is to the**sum**ofthe other two sides :: So is the difference of those sides : To the difference of the ...

Page 105

From half the

remainders continually together , and the square root of the last product will be

the area . That is , a + b + c - d a + b - itd a - b + c + d -atbtctd Х Х Х - the area .

From half the

**sum**of the four sides fubtract each side severally ; multiply the fourremainders continually together , and the square root of the last product will be

the area . That is , a + b + c - d a + b - itd a - b + c + d -atbtctd Х Х Х - the area .

Page 491

if A be put for the

the

c ; and c for the

...

if A be put for the

**sum**of the Extreme or First and Last Ordinates AB , NO ; B forthe

**sum**of the Even Ordinates CD , GH , IM , & c , viz . the second , fourth , fixth , &c ; and c for the

**sum**of all the rest ef , ik , & c , viz . the third , fifth , & c , or the Odd...

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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.