A Treatise on Mensuration, Both in Theory and Practice |
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Page vi
... cones ; and the relations of parabolas to rectilineal planes whofe quadratures had long before been determined by Euclid . He hath left us alfo his attempts upon the circle : he proved that a circle is equal to a right - angled triangle ...
... cones ; and the relations of parabolas to rectilineal planes whofe quadratures had long before been determined by Euclid . He hath left us alfo his attempts upon the circle : he proved that a circle is equal to a right - angled triangle ...
Page 175
... cone is a round pyra- mid ; having a circular bafe . 7. A fphere is a folid bounded by one continued convex fur- face , every point of which is equally diftant from a point with- in , called the the center . The fphere may be conceived ...
... cone is a round pyra- mid ; having a circular bafe . 7. A fphere is a folid bounded by one continued convex fur- face , every point of which is equally diftant from a point with- in , called the the center . The fphere may be conceived ...
Page 176
... cone having the fame bafe with the fegment , and its vertex in the center of the fphere . 16. A circular fpindle , is a folid generated by the revolution of a feg- ment of a circle about its chord , which remains fixed . 17. A wedge is ...
... cone having the fame bafe with the fegment , and its vertex in the center of the fphere . 16. A circular fpindle , is a folid generated by the revolution of a feg- ment of a circle about its chord , which remains fixed . 17. A wedge is ...
Page 182
... cone and cylinder of the fame bafe and altitude , the common altitude being equal to the radius of the bafe ; then the base , the surface of the cone , and the surface of the cylinder , are to one another as the numbers 1 , 2 , and 2 ...
... cone and cylinder of the fame bafe and altitude , the common altitude being equal to the radius of the bafe ; then the base , the surface of the cone , and the surface of the cylinder , are to one another as the numbers 1 , 2 , and 2 ...
Page 183
... cone , whofe flant fide is 20 , and the circum- ference of the bafe 9 . Here 10 × 990 is the convex furface required . PROBLEM IV . To find the Surface of the Fruftum of a Right Pyramid . Multiply the fum of the perimeters of the ends ...
... cone , whofe flant fide is 20 , and the circum- ference of the bafe 9 . Here 10 × 990 is the convex furface required . PROBLEM IV . To find the Surface of the Fruftum of a Right Pyramid . Multiply the fum of the perimeters of the ends ...
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Common terms and phrases
abfcifs againſt alfo altitude angle area fine area bafe baſe becauſe breadth bung cafe cafk circle whofe circumference cofine cone confequently conjugate Corol corollary correfponding curve defcribe dimenfions diſtance divided divifion draw ellipfe equal expreffed faid fame example fcale fecond fection feet fegment feries fhall fides figure fince find the area firft firſt fixed axe fluxion folid fome fphere fpheroid fpindle fquare fruftum ftands ftation fubtract fuch fuppofing furface gallons girt given half head diameter hence hoof hyperbola inches inftrument interfecting laft problem laſt lefs length meaſure multiply muſt nearly oppofite ordinate parabola paraboloid parallel perpendicular plane prob quotient radius rule SCHOLIUM ſhall Sliding Rule tangent thefe theſe thofe tranfverfe trapezium ufed uſed Verf whofe height whole whoſe
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.