QUEST. 7. A ladder, 40 feet long, may be fo planted, that it fhall reach a window 33 feet from the ground, on one fide of the street; and by turning it over, without moving the foot out of its place, it will do the fame by a window 21 feet high, on the other fide required the breadth of the street.

Anf. 56.649 feet. QUEST. 8. There are two columns left standing upright in the ruins of Persepolis; the one is 64 feet above the plane, and the other 50: In a right line between these stands an antient ftatue, the head of which is 97 feet from the fummit of the higher, and 86 from that of the lower column; the base of which measures juft 76 feet to the center of the figure's base required the distance between the tops of the two columns. Anf. 157 feet.

QUEST. 9. A may-pole, whofe top was broken off by a blast of wind, ftruck the ground at 15 feet distance from the foot of the pole: what was the height of the whole may-pole, fuppofing the length of the broken piece to be 39 feet Anf. 75 feet. QUEST. 10. Suppofe the breadth of a well at the top be 6 feet, and the angle formed by its fide and a vifual diagonal line from the edge at top to the oppofite fide at the bottom, 18° 30': required the depth of the well. Anf. 17.89 feet.

QUEST. II. At 85 feet distance from the bottom of a tower, the angle of its elevation was found to be 52° 30': required the altitude of the tower. Anf. 110 feet. QUEST. 12. At a certain place the angle of elevation of an inacceffible tower was 26° 30'; then measuring 75 in a direct line towards it, the angle was then found to be 51° 30': required the height of the tower, and its distance from the last station.

Anf.

height 62,

{distance 49.

G4

QUEST.

QUEST. 13. To find the distance of an inacceffible caftle gate, I measured a line of 73 yards, and at each end of it took the angle of pofition of the object and the other end, and found the one to be 90°, and the other 61° 45′ required the diftance of the castle from each ftation.

:

Anf. {135'8,

154.2.

QUEST. 14. From the top of a tower by the fea fide of 143 feet high, I obferved that the angle of depreffion of a fhip's bottom, then at anchor, was 55°; what was its diftance from the bottom of the wall? Anf. 204 56 feet.

QUEST. 15. How far at fea can the pike of Teneriff be seen, its height being 4 miles, and the radius of the earth 39787 miles? Anf. 178 miles. QUEST. 16. If a fhip, in the latitude of 50° north, fail 52 miles in the direction s wby s: what latitude is fhe arrived in, and how much farther to the weft? lat. 49° 16.8', weft 28.9 miles.

Anf.

QUEST. 17. Sailing w sw, I faw, at fome diftance, a point of land, which I fet, and found its bearing w by N; and after failing 6 leagues farther, I fet it again, and found its bearing N w by w. Required its diftance. Anf. 26.13 miles.

QUEST. 18. Obferving three fteeples, A, B, C, in a town at a diftance, whofe diftances afunder are known to be as follows, namely, AB 106, AC 202, and BC 131 fathoms, I took their angles of pofition from the place where I ftood D, which was nearest the steeple в, and found the angle ADB 13° 30', and the angle CDB 29° 50'. Required my diftance from each of the three steeples. DA 302.8 Anf. DB 214.8

[DA

DC 262.0

QUEST. 19. Suppofing my station to be fartheft from the fteeple в, required to find the distances from it, when the diftance AB is 9 furlongs, AC 12,

and BC 6 furlongs; alfo the angle ADB 33° 45', and

the angle CDB 22° 30'.

QUEST. 20.

DA 10.64 Anf. DB 15.64

DC 14.01

Two fhips fail from the fame port; the one fails ENE 85 miles, the other fails E by s till the first ship bears N w by w: what is the dif tance of the fecond fhip from the port, and alfo from the first ship? from the port 184.7

Anf.

{from the 1ft hip 123'4

QUEST. 21. Two ports lie east and weft of each other: a fhip fails from each, namely, the ship from the weft port fails NE 89 leagues, and the other fails 80 leagues, when the meets the former required the latter fhip's courfe, and the distance between the two ports. course 51° 52′

Anf.

{

distance 112.3

QUEST. 22. Two ships fail from a certain port; the one fails s by E 45 leagues, and the other ss w 64 leagues. What then are their bearings and diftance afunder?

Anf. {bearing 43° 14′

QUEST. 23. A fhip failing Nw, two iflands appear in fight, of which the one bore N, and the other wNW; but after failing 20 leagues, the former bore N E, and the latter w by s. What is the distance afunder of the two iflands?

Anf. 32.38 leagues.

PART

PART II.

OF SUPERFICIAL MENSURATION, OR THE MENSURATION OF PLANE FIGURES.

SECTION I.

OF THE AREAS OF RIGHT-LINED AND CIRCULAR

THE

FIGURES.

HE meafure of a plane figure is called its area. By the menfuration of plane figures is determined the extenfion of bodies as to length and breadth; fuch as the quantities of lands, and the works of many artificers.

Plane figures, and the furfaces of bodies, are measured by fquares; as fquare inches, or fquare feet, or fquare yards, &c; that is, fquares whofe fides are inches, or feet, or yards, &c. Our leaft fuperficial measure is the fquare inch, other fquares being. taken from it according to the proportion in the following table.

To find the Area of a Parallelogram, whether it be a Square, a Rectangle, a Rhombus, or a Rhomboid.

* Multiply the length by the height or perpendicular breadth, and the product will be the area. That is, AB X AC = the area.

Note. Because the length of a fquare is equal to its height, its area will be found by multiplying the fide by itself. That is AB X AB or AB is the area of the fquare.

EX

For, let ABCD be a rectangle; and let A its length AB and CD, and its breadth AD and BC, be each divided into as many equal parts, as is expreffed by the number of times they contain the lineal meafuring unit; and let all the oppofite points of divifion be connected by right D lines. Then, it is evident that, these

B

C

lines divide the rectangle into a number of fquares, each equal to the fuperficial meafuring unit; and that the number of thefe fquares is equal to the number of lineal meafuring units in the length, as often repeated as there are lineal measuring units in the breadth, or height; that is, equal to the length drawn into the breadth. But the area is equal to the number of squares or fuperficial measuring units; and therefore the area of a rectangle is equal to the product of its length and breadth.

Again, a rectangle is equal to an oblique parallelogram of an equal length and perpendicular height, by Euclid I. 36. Therefore the area of every parallelogram is equal to the product of its length and height. 2. E.D.