The description and use of the universall quadrat.: By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c.

Stirrup, Thomas.

Table of contents | Add to bookbag | How to cite

The Third Book.

<< Previous section Next section >>

CHAP. XXIV. The Latitude of the place, the Altitude and declination of the Sun being given, to finde the houre of the day,

THus in the oblique spherical Triangle ZP♉ in the Diagram of the 6 Chapter having the three sides, viz. ZP the complement of the Latitude 37 degrees 30 minutes and Z♉ the complement of the Suns Altitude 64 degrees 4 minutes with P♉ the complement of declinati∣on 78 degrees 30 minutes we may finde the angle ZP♉ the houre from the meridian by the 41 Chapter of the second Book, but by this Instrument more readily thus,

First, by the 16 Chapter, get the Suns height or de∣pression at the hour of 6, and if the declination be North take the distance betwixt this sine and the sine of the Al∣titude given, either by substraction, or with your com∣passes, this distance either count or place upon the con∣trary sine of the complement of the latitude, and thereto place the threed; the threed being thus placed, will cut the contrary sine of 90 degrees, at a right sine or parallel, which follow to the contrary sine of the Complement of declination, and thereto place the threed, so shall it cut the contrary sine of 90 degrees at the right sine of the houre from six. For,

As the cosine of the Latitude,
To the distance betwixt the sine of the height at six, and the sine of the Altitude given:

Page 174

So is the radius,
To a fourth sine.

Then,

As the cosine of declination,
To this fourth sine:
So is the radius,
To the sine of the houre from six.

Thus in the Diagram of the 6 Chapter, having the Suns declination EG or ♈O 11 degrees 30 minutes and the angle P♈B the latitude of the place 52 degrees 30 minutes, we have by the 16 Chapter the Suns height at 6 RO 9 deg. 6 min. the sine whereof is 158, the radius be∣ing 1000; this sine being compared with the sine of 25 deg. 56 min. 437 the sine of the Suns altitude Ra; and taking RO 158, out of Ra 437, there will remaine Oa 279; by which and the angle a♉o the complement of the Latitude, with the right angle at a, we may finde ♉O the houre from six.

For if we apply the threed to the intersection of the contrary sine of 37 deg. 30 min. with the right parallel of 279, it will cut the contrary sine of 90 degrees at the right sine of about 27¼ degrees, but seeing this 27¼ degrees which is O♉, is but upon the parallel of declination GO, therefore I place the threed again at the intersection of this 27¼ with the contrary sine of 78 deg. 30 min. the complement of declination GO, and it will cut the con∣trary sine of 90 deg. at the right sine of 27 deg. 54 min. and so much is ♈X or the angle ♈PX, the houre from six, which was required.

And here note that if the Altitude given be greater then the Altitude at six, then is the time found to the southward of six; but if it be lesser, then is it to the north∣ward.

Page 175

But if the declination be Southward, then adde the sine of his depression at six, to the sine of the Altitude given, and with the same proceed in all respects as before, and you shall have your desire.

All these kinde of propositions upon this Instrument, when you are well acquainted therewith, are sooner wrought then spoken.

<< Previous section Next section >>