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

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Page 510

... station point draw a line with the point of the compasses along the fiducial

edge of the index ; then

same by another , and so on till as many objects are

necessary .

... station point draw a line with the point of the compasses along the fiducial

edge of the index ; then

**set**another object or corner , and draw its line ; do thesame by another , and so on till as many objects are

**set**as may be thoughtnecessary .

Page 537

At all the places , which you would

flags at them of several colours , to distinguilh the places from one another ; fixing

them upon the tops of church steeples , or the tops of houses , or in the centres of

...

At all the places , which you would

**set**down in the map , plant long poles withflags at them of several colours , to distinguilh the places from one another ; fixing

them upon the tops of church steeples , or the tops of houses , or in the centres of

...

Page 567

So when 250 is to be multiplied by 56 : Having

56 be found on B , it is beyond the end of A ; therefore dividing it by 10 , I find that

opposite to the quotient 5-6 on B , is the division 1400 on A ; which being ...

So when 250 is to be multiplied by 56 : Having

**set**i on B to 250 on A , although56 be found on B , it is beyond the end of A ; therefore dividing it by 10 , I find that

opposite to the quotient 5-6 on B , is the division 1400 on A ; which being ...

Page 596

By the last chapter , the content was nearly 92 ale gallons : Hence , having

on N to 100 on ss , and against 10 on n found 23 on ss ; then

on A , and against 92 on B is found 21.2 ale gallons on A , for the quantity ...

By the last chapter , the content was nearly 92 ale gallons : Hence , having

**set**40on N to 100 on ss , and against 10 on n found 23 on ss ; then

**set**100 on B to 23on A , and against 92 on B is found 21.2 ale gallons on A , for the quantity ...

Page 603

of 23 . Or , by the other two lines ,

every number on d stands its square in the line c . So against 23 stands 529 ...

**Set**i on B to 23 on A ; then against 23 on B stands 529 on A , which is the squareof 23 . Or , by the other two lines ,

**set**i or 100 on c to the 10 on D , then againstevery number on d stands its square in the line c . So against 23 stands 529 ...

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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.