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. / By Thomas Stirrup, Philomathemat.

Title

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. / By Thomas Stirrup, Philomathemat.

Author

Stirrup, Thomas.

Publication

London :: Printed by R. & W. Leybourn, for Tho. Pierrpont, at the Sun in Pauls Church-yard,

1655.

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Subject terms

Astronomy

Dialing

Geometry

Navigation

Trigonometry

Link to this Item

https://name.umdl.umich.edu/A93912.0001.001 content_copy

Cite this Item

"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. / By Thomas Stirrup, Philomathemat." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A93912.0001.001. University of Michigan Library Digital Collections. Accessed June 3, 2024. content_copy

Contents

• title page
• To the READER.
• table of contents
  • The Contents of the first Book.
  • The Contents of the second Book.
  • The Contents of the third Book.
• illustrations
• The First Book.
  • CHAP. I. The description and making of the Universall Quadrat.
  • CHAP. II. The description of the back-side of the Universrl Quadrat.
  • CHAP. III. How to place the fixed Stars in the Sphere, and also in the outward Eclipticall Circle, for the speedy find∣ing of the houre of the night in all Latitudes.
  • CHAP. IV. To shew the Generall Use of the universall Quadrat.
  • CHAP. V. To divide a line given, into any number of equall parts.
  • illustration
  • CHAP. VI. To increase a line in a given proportion.
  • CHAP. VII. To diminish a line in a given proportion.
  • CHAP. VIII. To finde a proportion betwixt two or more Right lines.
  • CHAP. IX. To lay down sodainly 2, 3, or more Right lines in any proportion required.
  • CHAP. X. Having two lines given, to finde a third proportionall line to them.
  • CHAP. XI. Having three lines given to finde a fourth proportionall to them.
  • CHAP. XII. To finde a meane proportionall line between two right lines given.
    • section
    • To performe the some with numbers.
  • CHAP. XIII. To finde the square Root of a number given.
  • CHAP. XIV. To divide a line by extream and mean proportion.
  • CHAP. XV. Having either the greater or lesser segment, of a line divided by extream and mean proportion, to finde the other segment, and so consequently the whole line.
  • CHAP. XVI. To divide a right line given in power, according to any proportion required.
  • CHAP. XVII. To augment a superficies in a given proportion.
  • CHAP. XVIII. To diminish a superficies in a given proportion.
  • CHAP. XIX. To finde the perpendicular of an equilater Tri∣angle, the sides thereof being given.
  • CHAP. XX. How speedily to finde the perpendicular of a Right Angled Triangle, the sides being given; as also to finde the segments of the base, cut by the perpendicular.
  • CHAP. XXI. To finde the perpendicular of any Triangle, the three sides being given.
  • CHAP. XXII. To finde a proportion betweene two or more like superficies.
  • CHAP. XXIII. Two Geometricall Squares being given, to adde them together into one Square, and also to adde two circles together into one circle.
  • CHAP. XXIIII. Two squares or Circles being given, to substract the one out of the other, and to produce the re∣mainder in a third square.
  • CHAP. XXV. To make a square equall to any superficies given.
  • CHAP. XVI. Having the length and breadth of an oblong superficies given in perches, to finde the content in acres.
  • CHAP. XXVII. Having the length and breadth of an oblong su∣perficies given in Chaines, to finde the content in acres,
  • CHAP. XXVIII. The perpendicplar and base of a Triangle being given in perches, to finde the content in acres.
  • CHAP. XXIX. Having the perpendicular and base of a Triangle, given in Chains, to finde the content in acres
  • CHAP. XXX. Having the content of a superficies after one kind of perch, to finde the content of the same superficies according to another kinde of perch.
  • CHAP. XXXI. Having the plot of a plain with the content in acres, to finde the scale by which it was plotted.
  • CHAP. XXXII. Having the length of the furlong given in perches, to finde the bredth of the acre in perches.
  • CHAP. XXXIV. Having the length of the furlong given in Chains, to finde the breadth of the acre in Chains.
  • CHAP. XXXIV. Having the bredth of any Board given in inches, and the length in feet, to finde the content in feet.
  • CHAP. XXXV. Having the breadth of any board given in inches, to finde the length of a foot superficiall in inch measure.
  • CHAP. XXXVI. How to measure board which is taper grown, or wider at one end then at the other.
  • CHAP. XXXVII. Having the Circumference of a circle, to finde the Diameter.
  • CHAP. XXXVIII. Having the Diameter of a circle, to finde the circumference.
  • CHAP. XXXIX. Having the chord of any arch, with the perpendicular falling from the middle of the said arch to the chord, to finde the Diameter.
  • CHAP. XL. Having the circumference and Diameter of a circle given in inches, to finde the superficiall content in feet.
  • CHAP. XLI. To finde the superficiall content of any part or segment of a circle:
  • CHAP. XLII. Having the circumference of a circle, to find the side of a square equall to the same circle.
  • CHAP. LXIII. Having the diameter of a circle, to finde the side of a square equall to the same circle.
  • CHAP. XLIV. Having the breadth and depth of a squared solid given in inches, and the length in feet, to finde the content in feet.
  • CHAP. XLV. Having the breadth and depth of a squared solid given in inches, to finde the length of a foot solid in inch measure.
  • CHAP. XLVI How that prisma or peece of Timber, whose base or end is a Triangle, may be measured.
  • CHAP. XLVII. How that prisma or peece of Timber, whose base or end is a Rhombus, (or Diamond form) may be measured.
  • CHAP. XLVIII. How that prisma or peece of Timber whose base or end is a Rhomboides (or Diamond like) may be measured.
  • CHAP. XLIX. How that prisma or peece of Timber, whose base or end is a trapeziam may be measured.
  • CHAP. L. How that prisma or piece of Timber, whose base or end hath many sides, (as 5, 6, 7, 8, 9, 10, or more, so they be equall) may be measured.
    • section
    • A note to finde the centers of those equiangle figures.
  • CHAP. LI. Having the circumference and Diameter of a Cylinder given in inches, and the length in feet, to finde the content in feet.
  • CHAP. LII. Having the circumference and Diameter of a cylinder or round peece of Timber, in inches, to finde the length of a foot solid in inches.
  • CHAP. LIII. Having the circumference of a cylinder given in inches, and the length in feet, to finde the content in feet.
  • CHAP. LIV. Having the circumference of a cylinder given in inches, to finde the length of a foot solid in inch measure.
  • CHAP. LV. Having the Diameter of a cylinder given in inches, and the length in feet, to finde the content in feet.
  • CHAP. LVI. Having the Diameter of a cylinder given in inches, to finde the length of a foot solid.
  • CHAP. LVII. Having the circumference and Diameter of the base of a cone given in inches, with the altitude thereof in feet, to finde the solid content in feet.
  • CHAP. LVIII. Having the circumference of the base of a cone given in inches, and his altitude in feet, to finde the solid content in feet.
  • CHAP. LIX. Having the Diameter of the base of a cone given in inches, and his altitude in feet, to finde the solid content in feet.
  • CHAP. LX. Having the side and semidiameter of a cone, to finde his altitude or perpendicular falling from the top thereof, perpendicularly upon his base.
  • CHAP. LXI. Having the side of a segment of a cone, with the semidi∣ameter of each base or end thereof, to finde the altitude of te whole cone, as it were before it was cut off, with the altitude of the lesser cone which was cut off.
  • CHAP. LXII. How the segment cut off from any cone may be measured.
  • CHAP. LXIII. To finde the solid content of any pyramis.
• The Second Book.
  • section
    • CHAP. I. To finde the chord of any arch, the radius being gi∣ven, not exceeding the side of the quadrat.
    • CHAP. II. To finde the right sine of any arch given, the radius being put 1000.
    • CHAP. III. To finde the arch of any sine given, the radius being put 1000.
    • CHAP. IV. Any radius not exceeding the side of the quadrat being given, to finde the right sine of any arch or angle thereunto belonging.
    • CHAP. V. The right sine of any arch being given, to finde the radius.
    • CHAP. VI. The radius being given, with a streight line resembling a sine, to finde the quantitie of that unknown sine.
    • CHAP. VII. The use of these parallels, as they signifienaturall sines.
    • CHAP. VIII. The use of these parallels, as they signifie both Sines and Tangents.
    • CHAP. IX. The use of these parallels, as they are in their owne signification, joyned with their signification of Sines and Tangents.
  • Of the resolution of right lined Triangles
    • CHAP. X. Having three angles and one side to finde the other two sides.
    • CHAP. XI. Having two sides given, and one angle opposite to either of them; to finde the other two angles, and the third side.
    • CHAP. XII. Having two sides and the angle between them, to finde the two other angles and the third side.
    • CHAP. XIII. Having the three sides of a right lined Triangle, to finde the three angles.
    • CHAP. XIIII. In a rectangle Triangle having the angles and one of the sides given, to finde the other side and the base.
    • CHAP. XV. Having both sides of a rectangle Triangle, to finde the two angles and the base.
    • CHAP. XVI To finde a side and both the angles, by having the base and the other side given.
    • CHAP. XVII. To finde the sides by having the base, and the angles given.
    • CHAP. XVIII. In any right lined Triangle whatsoever, to finde a side by knowing the other two sides, and the angle contained by them.
    • CHAP. XIX. To finde an angle by knowing the three sides.
    • CHAP. XX. Of the ready reducing of hypothenusal to horizontal lines.
    • CHAP. XXI. To finde the height of an object accessible at one obsen∣vation. or the distance betwixt the top of the object and that point thereof which is level with your eye.
    • CHAP. XXII. To finde the height of an object inaccessible, at two observations.
  • Of the resolution of spherical Trian∣gles; and first of those which be right angled.
    • CHAP. XXIII. To finde a side by knowing the base, and the angle opposite to the required side.
    • CHAP. XXIV. To finde a side by knowing the base, and the other side.
    • CHAP. XXV. To finde a side, by knowing the two oblique angles.
    • CHAP. XXVI To finde the base, by knowing both the sides.
    • CHAP. XXVIII. To finde an angle, by knowing the other oblique angle, and the side opposite to the inquired angle.
    • CHAP. XXIX. To finde an angle, by knowing the other oblique angle, and the side opposite to the angle given.
    • CHAP. XXX. To finde an angle, hy knowing the base, and the side opposite to the inquired angle.
    • CHAP. XXXI. To finde a side, by knowing the other side, and the angle opposite to the inquired side.
    • CHAP. XXXII. To finde a side, by knowing the other side, and the angle next to the inquired side.
    • CHAP. XXXIII. To finde a side by knowing the base, and the angle next to the inquired side.
    • CHAP. XXXIV. To finde the base by knowing the oblique angles.
    • CHAP. XXXV. To finde the base, by knowing one of the sides, and the angle next the same side.
    • CHAP. XXXVI. To finde an angle by knowing both the sides.
    • CHAP. XXXVII. To finde an angle, by knowing the base, and the side next to the inquired angle.
    • CHAP. XXXVIII. To finde an angle, by knowing the other oblique angle, and the base.
  • In any Spherical Triangle whatsoever.
    • CHAP. XLI. To finde a side opposite to an angle given, by knowing one side, and two angles, the one opposite to the given side, the other to the side required.
    • CHAP. XL. To finde an angle opposite to a side given, by knowing one angle and two sides, the one opposite to the given angle, the other to the angle required.
    • CHAP. XLI. To finde an angle by knowing the three sides.
    • CHAP. XLII. To finde a side by knowing the three angles.
    • CHAP. XLIII. To finde a side, by knowing the other two sides, and the angle contained by them.
    • CHAP. XLIV. To finde a side by knowing the other two sides, and one angle next the inquired side.
    • CHAP. XLV. To finde a side, by knowing one side, and the two angles next the inquired side.
    • CHAP. XLVI. To finde a side by knowing two angles, and the side inclosed by them.
    • CHAP. XLVII. To finde an angle by knowing the other two angles, and the side inclosed by them.
    • CHAP. XLVIII. To finde an angle, by knowing the other two angles, and one of the sides next the inquired angle.
    • CHAP. XLIX. To finde an angle, by knowing two sides, and the angle conteined by them.
    • CHAP. L. To finde an angle, by knowing the two sides next it, and one of ahe other angles.
    • CHAP. LI. In a right angled triangle, having the base and one of the oblique angles, to finde the two sides, and the other angle.
    • CHAP. LII. By knowing the base and one of the sides, to finde the other side, with both the oblique angles.
    • CHAP. LIII. Having one side, and one of the oblique angles of a right an∣gled triangle, to finde the base, the other side, and the other oblique angle
    • CHAP. LIV. Having the two sides of a right angled triangle, to finde the base, and the two oblique angles
    • CHAP. LV. Having the two oblique angles, of a right angled Triangle, to finde a side opposite to either of them.
    • CHAP. LVI. Having the three sides of any spherical Triangle, to finde an angle opposite to any of them.
    • CHAP. LVII. To finde a side, by knowing the other two sides, and the angle comprehended.
    • CHAP. LVIII. To finde a side, by knowing the other two sides, and one of the angles next the inquired side.
    • CHAP. LIX. Having two sides and one angle, to finde any of the other two angles.
    • CHAP. LX. Having either all three angles to finde a side, or having two angles and one side, to finde any of the other two sides.
• The Third Book.
  • CHAP. I. To finde the Suns altitude, by the shadow of a Gnomon set perpendicular to the Horizon.
  • CHAP. II. The height of the Sun being given, to finde the length of the right shadow.
  • CHAP. III. To finde the Altitude of the Sun by the shadow of a Gnomon, standing at right angles with any perpendicular wall; in such manner that it may lie parallel to the Horizon.
  • CHAP. IV. The Height of the Sun being given, to finde the length of the contrary shadow.
  • CHAP. V. Having the distance of the Sun from the next Equinoctial point, to finde his declination.
  • CHAP. VI. How to finde the latitude of a place, or the Poles eleva∣tion above the Horizon, the declination of the Sun being given.
  • CHAP. VII. How to get the Declination of the Sun, or any Star, Planet, or Comet by observation in a known latitude.
  • CHAP. VIII. The Declination of the Sun, and the quarter of the Ecliptique which he possesseth being given, to finde his true place.
  • CHAP. IX. Having the latitude of the place, and the distance of the Sun from the next Equinoctial point, to finde his Amplitude.
  • CHAP. X. Having the Latitude of the place, and the declination of the Sun or Star to finde his Amplitude.
  • CHAP. XI. Having the amplitude and declination of the Sun, to finde the elevation of the Pole above the Horizon.
  • CHAP. XII. The elevation of the Pole, and the amplitude of the Sun be∣ing given, to finde his declination.
  • CHAP. XIII. Having the Latitude of the place, and the declination of the Sun, to finde his height in the vertical circle, or when he shall come to be due East or West.
  • CHAP. XIV. Having the latitude of the place, and the distance of the Sun from the Equinoctial point, to finde his height in the vertical circle.
  • CHAP. XV. Having the Latitude of the place, and the declination of the Sun, to finde the time when the Sun commeth to be due East or West.
  • CHAP. XVI. Having the Latitude of the place, and the declination of the Sun, to finde what altitude the Sun shall have at the houre of six.
  • CHAP. XVII. Having the latitude of the place, and the declination of the Sun, to finde what Azimuth the Sun shall have at the houre of six.
  • CHAP. XVIII. Having the Latitude of the place, and the declination of the Sun, to finde the Ascensional difference; and thereby the Time of Sun-rising and setting, with the diurnal and nocturnal arches.
  • CHAP. XIX. Having the latitude of the place, & the declination of the Sun, to finde the time of the beginning or ending of twilight.
  • CHAP. XX. Having the distance of the Sun from the next Equinoctial point, to finde his right ascension.
  • CHAP. XXI. Having the right ascension of the Sun or Star, together with the difference of their Ascensions, to finde the oblique Ascension and descension.
  • CHAP. XXII. Having the Azimuth, the Suns Altitude, and the declina∣tion, to finde the hour of the day.
  • CHAP. XXIII. Having the houre of the day, the Suns Altitude, and the de∣clination, to finde the Azimuth.
  • CHAP. XXIV. The Latitude of the place, the Altitude and declination of the Sun being given, to finde the houre of the day,
  • CHAP. XXV. The Latitude of the place, the Declination and Altitude of the Sun being given, to finde the Azimuth.
  • CHAP. XXVI. The place of the Sun being given, to finde his declination.
  • CHAP. XXVII. The declination of the Sun being given, to finde his place in the Ecliptique.
  • CHAP. XXVIII. The place of the Sun being given, to finde his Right Ascension.
  • CHAP. XXIX. Having the latitude of the place, with the place of the Sun in the Ecliptick, to finde his Amplitude.
  • CHAP. XXX. Having the latitude of the place, with the declination of any Star, to finde his Amplitude.
  • CHAP. XXXII. Having the Declination and Amplitude of the Sun, to finde the latitude of the place.
  • CHAP. XXXII. The latitude of the place, and the amplitude of the Sun being given, to finde his Declination.
  • CHAP. XXXIII. Having the latitude of the place, and the Declina∣tion of the Sun, to finde his height in the vertical Circle.
  • CHAP. XXXIV. Having the latitude of the place, and the Declination of the Sun, to finde the time of his comming to the East or West Points.
  • CHAP. XXXV. Having the latitude of the place, and the Declination of the Sun, to finde his height at the hour of six.
  • CHAP. XXXVI. Having the latitude of the place, and the Declination of the Sun, to finde his Azimuth at the hour of six.
  • CHAP. XXXVII. Having the latitude of the place, and the Declination of the Sun, to finde the Ascensional difference, and consequently the time of Sun-rising and setting, with the Diurnal and Nocturnal arches.
  • CHAP. XXXVIII. Having the latitude of the place, and the declination of the Sun, to finde the time of the beginning and ending of twilight.
  • CHAP. XXXIX. The latitude of the place, the altitude and declination of the Sun being given, to finde the houre of the day.
  • CHAP. XL. The latitude of the place, the Suns altitude and Declination being given, to finde his Azimuth.
  • CHAP. XLI. The longitude and latitude of any planet or fixed star being given, to sinde his Declination and right Ascension.
  • CHAP. XLII. Having the declination and right ascension of any fixed Star, to finde his longitude and latitude.
  • CHAP. XLIII. To finde the culmination, or southing, of any of the fixed Stars, as also of the Moon and other Planets. First, for the fixed Stars.
  • CHAP. XLIV. To finde the time of the rising or setting, of any of the fixed Stars, and also of the moon or other planets.
  • CHAP. XLV. To finde the exact hour of the night speedily by the Stars.
    • section
    • The 16 of November 1652, I made these two following ob∣servations by the planet Venus in the day time, as to the finding of the houre by the Stars, shee being about her greatest distance from the Sun.
  • CHAP. XLVI. To finde how many minutes or miles, answer to one degree of longitude, in any latitude required.
  • CHAP. XLVII. To finde what difference of longitude be longeth to one degree or 20 leagues of distance, upon any parallel of latitude.
  • CHAP. XLVIII. To finde how many leagues do answer to one degree of latitude, upon any Romb required.
  • CHAP. XLIX. To finde how much any ship hath raised or depressed the Pole, knowing the course she hath made, and the leagues shee hath sailed.
  • CHAP. L. By the Rumb and both latitudes to finde the distance upon the Rumb.
  • CHAP. LI. By the distance and both latitudes, to finde the rumb.
  • CHAP. LII. By the Rumb and difference of latitudes, to finde the difference of longitude.
  • CHAP. LIII. By the distance of latitude and leagues sailed, to finde the difference of longitude.
  • CHAP. LIV. By the difference of latitude, and difference of longitude, to finde the Rumb leading from the one to the other.
  • CHAP. LV. By one latitude, Rumb, and distance, to finde the difference of latitude, and also of longitude.
  • CHAP. LVI. By the longitude and latitude of two places, to finde their distance upon the Rumb.
  • CHAP. LVII. By the way of the Ship, and two angles of position, to finde the distance betweene the ship and the land.
  • CHAP. LVIII. To finde the distance of any Ship from you, your selfe stand∣ing upon some high clift or platform by the Sea coast, the height of the said platform a∣bove the water being known.
  • CHAP. LIX. How by this Instrument, from a high Platform, to measure the distance of any two ships on the sea, or other marks on the land, howsoever they be situated, and that right speedily.