Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
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Page vi
... Primitive Prob . 5. To measure any Spherical Angle Prob . 6. To divide any Great Circle into its grees Prob . 7. To draw any parallel Circle 45 46 proper De- 48 - 49 Prob . 8. To draw a Great Circle perpendicular to any other Prob . 9 ...
... Primitive Prob . 5. To measure any Spherical Angle Prob . 6. To divide any Great Circle into its grees Prob . 7. To draw any parallel Circle 45 46 proper De- 48 - 49 Prob . 8. To draw a Great Circle perpendicular to any other Prob . 9 ...
Page 3
... Primitive Circle is that defcribed on the Plane of the Projection , and within which the Projection is finifhed , as RPHE . XII . A Right Circle is that whofe Plane ftands at Right Angles with the Plane of the Projection , and paffeth ...
... Primitive Circle is that defcribed on the Plane of the Projection , and within which the Projection is finifhed , as RPHE . XII . A Right Circle is that whofe Plane ftands at Right Angles with the Plane of the Projection , and paffeth ...
Page 5
... Primitive EN 25 , and the Oblique Circle SAN ; for they pass thro ' , and interfect each other in the Poles N and S. See Fig . 4 . • ; XXVI . The Equinoctial or Equator , is a Great Circle every way equally diftant ( viz . 90 Degrees ) ...
... Primitive EN 25 , and the Oblique Circle SAN ; for they pass thro ' , and interfect each other in the Poles N and S. See Fig . 4 . • ; XXVI . The Equinoctial or Equator , is a Great Circle every way equally diftant ( viz . 90 Degrees ) ...
Page 22
... primitive Circle AC BD ; From the Line of Chords fet off 20 cutting the Oblique Circle in G ; Then the Part GH will be made 20 ° in the Oblique Circle , as required . 2. E. F. PROBLEM IV . To project , on the Plane of the Solftitial ...
... primitive Circle AC BD ; From the Line of Chords fet off 20 cutting the Oblique Circle in G ; Then the Part GH will be made 20 ° in the Oblique Circle , as required . 2. E. F. PROBLEM IV . To project , on the Plane of the Solftitial ...
Page 24
... Primitive , as taught in Prcb . 2. Alfo any of thofe Ellipfes may be divided into their proper Degrees , by Prob . 3 . 2002 TO PRO- • PROBLEM VI . To divide the Ecliptic according to 24 . Problems of the Orthog . Projection . To ...
... Primitive , as taught in Prcb . 2. Alfo any of thofe Ellipfes may be divided into their proper Degrees , by Prob . 3 . 2002 TO PRO- • PROBLEM VI . To divide the Ecliptic according to 24 . Problems of the Orthog . Projection . To ...
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Common terms and phrases
adjacent Angle alfo Altitude Analemma Analogy Arch Azimuth Bafe Baſe becauſe BIFH Cafe Center Chords Circles of Latitude Co-fine Co-tangent Colure Complement confequently Cufp Declination defcribe Degrees Demonftration Dial Diameter Diſtance draw E. D. THEOREM Eaft Ecliptic equal Equinoctial faid fame fhall fhew find the Angle find the Hypothenufe find the Leg find the Side firft firſt folving fuch fuppofe given the Side Globe greateſt half Sum Half-Tangent Horizon Hour-Lines Houſes Interfection laft Latitude leffer lefs Longitude meaſured Meridian muſt North Numbers Oblique Circle oppofite paffeth Parallel Perpendicular Plane recline Pofition Point Pole Prime Vertical Prob PROBLEM Projection Quadrant Radius Reclining Plane Right Afcenfion Right Line Right-angled Spherical Triangles Scheme Semicircle Sine Sine of half Sphere Spherical Angle Spherical Trigonometry Sun's Tangent of half thefe theſe thofe thoſe Tropic of Capricorn Weft Wherefore whofe
Popular passages
Page 75 - The three angles of a spherical triangle are together greater than two right angles and less than six right angles. Let A, B, C be the angles of a spherical triangle ; let a', b', o' be the sides of the polar triangle. Then by Art. 30, a...
Page 185 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 186 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles.
Page 186 - The cosine of half the sum of two angles of a spherical triangle is to the cosine of half their difference as the tangent of half the included side is to the tangent of half the sum of the other two sides.
Page 186 - The sine of half the sum of two angles of a spherical triangle is 'to the sine of half their difference as the tangent of half the included side is to the tangent of half the difference of the other two sides.
Page 241 - It commences in the morning and ends in the evening, when the sun is 18° below the horizon.
Page 5 - Equinoctial (counted from the beginning of Aries) which cometh to the Meridian with the Sun or Stars, or with any portion of the Eclyptick.
Page 365 - Dialogue, adapted purpofely to the Capacities of the Youth of both Sexes ; and adorned and illuftrated with variety of Copper- Plates.
Page 75 - Side *»» is the Supplement of the Angle H, and the Angle E of the Side G D.
Page 205 - Superficies to M ; And, as two right Angles are to F, So is half the fpherical Superficies to K.