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To measure beiylsts and distances by the geometrical square.

When the plane is horizontal, the instrument is to be supported and placed horizontally at any point A, and it is to be turned till the remote point F, whose distance is to be measured, is seen through the fixed sights; then turn the dex, till, through the fights upon it, you see any acceslible object B; then place the inftrument at the point B, directing the fixed fights to the first station A, and the moveable ones to the point T'; and if the index cut the reclined side of the square, as in the point E, then, from similar triangles, ES : SB :: as BA : AG; Lut if the index cut the right side of the square K, it will be BR:RK::BA: AF. In either of thefe cases, the distance required may be found by the rule of three *.

Perpendicular heights, when accessible, may be obtained by the quadrant only. For example, If you wanted the height of

house, tree, &c. approach towards or retire from the object, till it subtends an angle of 45°; then shall the height of the object be equal to its horizontal diftance. Euclid, I. 6.

A similar observation may be made of the other instruments used for heights and distances; but this, and many more, will daily occur in practice.

* The fide DE is called the right side, E the reclined Gide.

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CONTAINING,

I. A TABLE OF THE LOGARITHMS OF NUMBERS

FROM I TO 10000,

II. A TABLE OF LOGARITHMIC SINES, TAN.

GENTS, SECANTS, AND VERSED SINES,
TO EVERY DEGREE AND MINUTE OF THE QUA-
DRANT.

III. A TABLE OF LOGARITHMIC SINES, TAN

GENTS, AND SECANTS, TO EVERY POINT,
HALF POINT, AND QUARTER POINT OF THE
COMPASS

A TABLE of the LOGARITHMS of NUMBERS from 1 to 10000,

Log. No

Log Log No Log. (No. Log. 10.ooooo 211.32222 471.61278 611.785331 811.90848 20.30163 22 1.34242| 42 1.62325 621.79239 82 1.91381 30.47712 231.36173 431.63347 631.7993. 831.91908 40.60206241.38021 44 1.64345 64/1.806181841.92428 5 0.69897 25 1.39794 45 1.65321 65 1.81291_851.92942) 60.77875 261.41497 46,1.00276 661.81954 861.93450 7 0.8451C 271.43136 47 1.67220 671.82607 871.93952 8c 0.903091 28f1.44786 481.68124 68 1.83251| 88 1.94448 90.95424 29 1.46240 49 1.69020 69 1.83885) 891.94939 101.00pool 30 1.47712 501.69897 70 1.84510901.95424 II 1.04139 31 1.49136 511.707571 71 1.85120 911.95904 121.07918 321.50515 52 1.71600) 72 1.85733 921.96379 131.11394 331.51851 531.72428 731.86332 931.96848 141.14613 341.53148 541.73239 74 1.869231 941.973:3) 15 1.17609 35/1.54407 551.74036_75 1.87506 951.97772 16 1.20412 367.55636 56 1.74819 761.880811 9011.78227 171.23045 37 1.56820) 571.75587| 77 1.886499, 1.98677 181.25527) 38|1.579781 581.76343 78|1.89209 9811.99123 191.27875 39 1.59100 5911.77085 79 1.89763 90|1.9956; 20 1.3010; 40/1.60200 601.77814) 801.903071102.00000

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PROBLEM IX.

To meafure heights and distances by the geometrical square.

When the plane is horizontal, the instrument is to be fupported and placed horizontally at any point A, and it is to be turned till the remote point F, whose distance is to be measured, is seen through the fixed sights; then turn the dex, till, through the fights upon it, you see any accessible object B; then piace the instrument at the point B, directing the fixed fights to the first station A, and the moveable ones to the point 1 ; and if the index cut the reclined side of the square, as in the point E, then, from similar triangles, ES : SB :: as BA : AG; Lut if the index cut the right side of the square K, it will be BR:RK ::BA: AF. In either of these cases, the distance required may be found by the rule of three *.

Perpendicular heights, when accessible, may be obtained by the quadrant only. For example, If you wanted the height of a house, tree, &c. approach towards or retire from the object, till it subtends an angle of 45° ; then shall the height of the object be equal to its horizontal dittance. Euclid, I. 6.

A fimilar observation may be made of the other instruments used for heights and distances; but this, and many more, will daily occur in practice.

The side DE is called the right side, E the reclined Gde.

TABLES.

CONTAINING,

1

I. A TABLE OF THE LOGARITHMS OF NUMBERS

FROM I TO 10000.

II. A TABLE OF LOGARITHMIC SINES, TAN.

GENTS, SECANTS, AND VERSED SINES,
TO EVERY DEGREE AND MINUTE OF THE QUA-
DRANT.

III. A TABLE OF LOGARITHMIC SINES, TAN

GENTS, AND SECANTS, TO EVERY POINT,
HALF POINT, AND QUARTER POINT OF THE
COMPASS

A TABLE of the LOGARITHMS of NUMBERS from 1 to 10000,

:

¡N!!! Log. No Log. Log No. Log. No. Log.

I c.00000 211.32222 4111.612781 61 1.78533 811.90848 210.30103 221.34242 42 1.62325 621.79239 82 1.91381 30.47712 23 1.36173) 431.63347 63 1.79934 831.91908

0.60206241.38021 44 1.64345 641.80618 841.92428 5 0.69897 25 1.39794 45 1.65321 651.81291_851.92942 60.77855 261.41497 46 1.06276 66 1.81954 801.93450 70.8451C 271.43136 47 1.67220 67 1.82607 87 1.93952 80.90309 281.44786 481.68124 68 1.83251 881.94448 90.95424 29 1.46240 49 1.69020 69 1.83885 891.94939 101.00poo 301.47712 50 1.69897 701.84510_901.95424) II 1.04139 311.49130 S11.70757 711.85120 911.95904 121.07918 321.50sis 521.71600) 7211.85733 921.96379 131.11394 331.51851 531.72428 7311.86332 93 1.96848 141.14613 341.53148 541.73239 74 1.86923 94.973:3 151.17609 35/1.54407 551.74036_251.87506 2:1.97772 16 1.20412 3617.55636 56 1.74819 761.88081| 901.98227 171.2304,5 37 1.56820 3711.75587| 77 1.88649 91.98677 181.255271 38|1.5797581.76343 786.89204 9811.99123 191.27875 391.5910 591.79085 79 1.89763 991.99563 2011.30103| 40|1.60200 601.778141 811.903071102.00000

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