A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.

Of Oblique Triangles. PROB. VII.

The three Sides given, to find the Angles.

ELevate the Pole of the Globe above the Horizon to the Complement of one of the given Sides and screw the Qua∣drant of Altitude in the Zenith, so shall that given Side be com∣prehended between the Pole and the Quadrant of Altitude; Then count from the Pole upon the first Meridian the measure of the Second Side, and there make a prick; Count also from the Ze∣nith upon the Quadrant of Altitude downwards the measure of the third Side, and make there on the edge of the Quadrant of Altitude another prick; Then turn the Globe and Quadrant of Altitude till you can joyn these two pricks together; so shall your Triangle be made on the Globe: And then the number of de∣grees of the Equinoctial comprehended between the first Meridi∣an

and the Brasen Meridian shall be the measure of the Angle at the Pole: The Arch of the Horizon comprehended between the Quadrant of Altitude and the intersection of the Brasen Meri∣dian with the Horizon on that side the Pole is elevated, shall be the measure of the second Angle: And for finding the third An∣gle, you must turn the Triangle, as by Prob. 1.

Example.

In the Triangle A B C annexed, The Side A B contains 38. degrees 30. minutes, the side B C 25. degrees, and the side A C 60. degrees; I would measure these Angles; I place one of these sides upon the Meridian, viz. A B 38. degrees 30 mi∣nutes, the Complement of 38. degrees 30. minutes is 51 de∣grees 30. minutes; Therefore I Elevate the Pole 51. degrees 30. minutes above the Horizon, so shall the Zenith be distant from the Pole 38. degrees 30. mi∣nutes; here I screw the Quadrant of Altitude and count down∣wards on it the measure of the side B C 25. degrees, and there I make a prick: Then from the Pole I count on the first Meridi∣an 60. degrees, the measure of the side A C, and there I make a∣nother prick: Then I turn the Globe and Quadrant of Alti∣tude backwards or forwards till these two pricks are joyned to∣gether; so shall the Triangle A B C be made on the Globe: The arch of the Brasen Meridian comprehended between the Pole and Zenith shall represent the side A B; the Arch of the Quadrant of Altitude comprehended between the first Meridian and the Brasen Meridian shall represent the side B C; and the Arch of the first Meridian comprehended between the Pole and the Quadrant of Altitude shall represent the side A C; The Pole shall represent the Angle A, the Zenith the Angle B; and the intersection of the first Meridian with the Quadrant of Altitude shall represent the Angle C. The Angle at the Pole is measured in the Equator; for the degrees comprehended between the first Meridian and the Brasen Meridian being 17. degrees 15. minutes shews 17. degrees 15. minutes to be the measure of the Angle A. The Angle at the Zenith is measured in the Horizon; for

the degrees comprehended between the Intersection of the Brasen Meridian with the Horizon on that side the Pole is Elevated be∣ing 142. degrees 42. minutes, shews that 142. degrees 42. mi∣nutes is the measure of the Angle B, Thus two angles are found; the third is wanting: which I find thus,

[illustration]

I turn the Triangle, placing either A or C in the Zenith. Ex∣ample: I place A at the Zenith, which before was at the Pole; so shall C be at the Pole, and B at the Intersection of the first Meridian and the Quadrant of Altitude, and the side A C shall be comprehended between the Pole and Zenith: The side A C contains 60. degrees; its Complement to 90 is 30. degrees; therefore I Elevate the Pole of the Globe 30. degrees above the Horizon; so shall 60. degrees be in the Zenith; therefore to 60. degrees I screw the Quadrant of Altitude and count on it down∣wards the measure of the other side next the Zenith, viz. 38. degrees 30. minutes; and there I make a prick: Then from the Pole on the first Meridian I count the measure of the last side, viz. 25. degrees, and there I make another prick: Then I turn the Globe and Quadrant of Altitude (as before) till these two pricks joyn; so is the Triangle altered on the Globe: For the Arch of the Brasen Meridian comprehended between the Pole and Zenith which before was 38. degrees 30. minutes, is now 60. de∣grees; the Arch of the Quadrant of Altitude Comprehended be∣tween the first Meridian and the Brasen Meridian, which before was 25 degrees, is now 38. degrees 30. minutes; and the Arch of the first Meridian comprehended between the Quadrant of Altitude and the Pole, which before was 60. degrees is now 25. degrees. Thus the Angle C being now at the Pole, its measure is found in the Equinoctial, viz. that Arch comprehended be∣tween the first Meridian and the Brasen Meridian, which is 25. degrees 24. minutes; and the measure of the Angle A, which is now in the Zenith, having its sides, the one an Arch of the Bra∣sen Meridian, the other an Azimuth, (or which is all one) an Arch of the Quadrant of Altitude, is measured in the Horizon, as all Azimuths are, and found 17. degrees 15. minutes, as before.