Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
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Page i
... Meridian , the Horizon , the Ecliptic , the Equinoctial , the Tropic of Capricorn , and of an Oblique Circle . V. Forty One Theorems explaining the Nature and Rationale of Spherical Triangles . VI . A Synopsis of all the Cafes of a ...
... Meridian , the Horizon , the Ecliptic , the Equinoctial , the Tropic of Capricorn , and of an Oblique Circle . V. Forty One Theorems explaining the Nature and Rationale of Spherical Triangles . VI . A Synopsis of all the Cafes of a ...
Page vi
... Meridian 2. On the Plane of the Horizon of London 3. On the Plane of the Ecliptic 4. On the Plane of the Equinoctial 5. On the Plane of the Tropic of Capricorn 6. On the Plane of any Oblique Circle Chap . VII . 56 62 65 68 70 Containeth ...
... Meridian 2. On the Plane of the Horizon of London 3. On the Plane of the Ecliptic 4. On the Plane of the Equinoctial 5. On the Plane of the Tropic of Capricorn 6. On the Plane of any Oblique Circle Chap . VII . 56 62 65 68 70 Containeth ...
Page ix
... Meridian Angle 256 257 Prob . 26. To find the Declination of the Culmina- ting Point Prob . 27. To find the Altitude thereof ibid . 258 ibid . Prob . 28. To find the Altitude of the Nonagefima Degree - Prob . 29. To find the Place ...
... Meridian Angle 256 257 Prob . 26. To find the Declination of the Culmina- ting Point Prob . 27. To find the Altitude thereof ibid . 258 ibid . Prob . 28. To find the Altitude of the Nonagefima Degree - Prob . 29. To find the Place ...
Page xi
... Meridian , all in the Arches of a Great Circle of the Globe , and is therefore called , Great Circle Sailing Chap . V. 305 Containeth the Method of Making and Sailing by the Glo- bular Chart . With regard to its Conftruction there is ...
... Meridian , all in the Arches of a Great Circle of the Globe , and is therefore called , Great Circle Sailing Chap . V. 305 Containeth the Method of Making and Sailing by the Glo- bular Chart . With regard to its Conftruction there is ...
Page 7
... Meridian with the Hori- zon ; fuch is HBO . XXXVII . The Tropics are two fmall Circles paral- lel to the Equinoctial , and diftant ( on each Side ) there- from 23 ° 29 ′ ; they are the Limits of the Sun's great- eft Declination from the ...
... Meridian with the Hori- zon ; fuch is HBO . XXXVII . The Tropics are two fmall Circles paral- lel to the Equinoctial , and diftant ( on each Side ) there- from 23 ° 29 ′ ; they are the Limits of the Sun's great- eft Declination from the ...
Contents
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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.