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

### From inside the book

Results 1-5 of 6

Page 32

To make a Square

F G BE be

C D radius . Ao describe a semicircle , and produce Bc to E Β ο Η A meet it at F.

To make a Square

**equal**to a given Rectangle ABCD . Produce one side , AB , tillF G BE be

**equal**to the other fide Bc . - Bifect AE in 0 ; on which as a center , withC D radius . Ao describe a semicircle , and produce Bc to E Β ο Η A meet it at F.

Page 91

Because the length of a square is

multiplying the side by itself . — That is AB X AB or AB ' is the area of the square .

E XDEMONSTRATION . For , let ABCD be a rectangle ; and let A B its length ab ...

Because the length of a square is

**equal**to its height , its area will be found bymultiplying the side by itself . — That is AB X AB or AB ' is the area of the square .

E XDEMONSTRATION . For , let ABCD be a rectangle ; and let A B its length ab ...

Page 152

Whenc ?, if the two sides AC , CB , of the triangle be

lunes will , also , be

the segment si = femicircle AQCA - AACD = double the leg . AWDA , or double ...

Whenc ?, if the two sides AC , CB , of the triangle be

**equal**to each other ; the twolunes will , also , be

**equal**, and each lune L i**equal**to the A ACD ; and thereforethe segment si = femicircle AQCA - AACD = double the leg . AWDA , or double ...

Page 164

The four sides of a field , whose diagonals are

be 25 , 35 , 31 , and 19 poles , in a successive order ; from whence the content of

the field is required . B. ITIN Construction . Make AB and ac perpenD dicular to ...

The four sides of a field , whose diagonals are

**equal**to each other , are known tobe 25 , 35 , 31 , and 19 poles , in a successive order ; from whence the content of

the field is required . B. ITIN Construction . Make AB and ac perpenD dicular to ...

Page 366

Charles Hutton. their altitudes are likewise the same ; and therefore the parabolic

area will be

to denote its altitude , and b its base . It may farther be observed , that if the ...

Charles Hutton. their altitudes are likewise the same ; and therefore the parabolic

area will be

**equal**to į of its altitude multiplied by its base ; that is = bab ; putting ato denote its altitude , and b its base . It may farther be observed , that if the ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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.