Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
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Page 1
... whofe Superficies is equi- distant from its Center . See Fig . 1 . II . A Sphere is an Artificial Instrument confifting of various Circles , Great and Small , put together in a VOL . II . B pro- proper Order and Pofition . And becaufe ...
... whofe Superficies is equi- distant from its Center . See Fig . 1 . II . A Sphere is an Artificial Instrument confifting of various Circles , Great and Small , put together in a VOL . II . B pro- proper Order and Pofition . And becaufe ...
Page 3
Benjamin Martin. IX . A Great Circle of the Sphere , is that whofe Plane paffeth through the Center thereof , and whofe : Center is the fame with that of the Sphere ; it also di- videth the Globe or Sphere into two equal Parts ; as Pe Oq ...
Benjamin Martin. IX . A Great Circle of the Sphere , is that whofe Plane paffeth through the Center thereof , and whofe : Center is the fame with that of the Sphere ; it also di- videth the Globe or Sphere into two equal Parts ; as Pe Oq ...
Page 5
... those twelve constellated Animals , whofe Names and Cha- racters follow . 1. Aries , the Ram , V. 2. Taurus , the Bull , . 3. Gemini , the Twins , II , 4. Can- cer , 3 . · cer , the Crab , . 5. Leo , Principles of the Spherical Doctrines ...
... those twelve constellated Animals , whofe Names and Cha- racters follow . 1. Aries , the Ram , V. 2. Taurus , the Bull , . 3. Gemini , the Twins , II , 4. Can- cer , 3 . · cer , the Crab , . 5. Leo , Principles of the Spherical Doctrines ...
Page 17
... whofe longer Diameter is DC , and the fhorter FG . 2. E. D. THEOREM X. An Ellipfis ftanding at Right - Angles with the Plane of the Projection , is projected into a Right Line ; if it be parallel to the Plane of the Projection , ' tis ...
... whofe longer Diameter is DC , and the fhorter FG . 2. E. D. THEOREM X. An Ellipfis ftanding at Right - Angles with the Plane of the Projection , is projected into a Right Line ; if it be parallel to the Plane of the Projection , ' tis ...
Page 18
... whofe Co - fine is DE FC . Make the given Line Radius DC : Then , as the given Right Line DC Is to its Projection FC DE :: Radius : to the Co - fine of AC D. Q. E. D. Corollary . Hence the Radius DC , the Arch DG , and its right Sine ...
... whofe Co - fine is DE FC . Make the given Line Radius DC : Then , as the given Right Line DC Is to its Projection FC DE :: Radius : to the Co - fine of AC D. Q. E. D. Corollary . Hence the Radius DC , the Arch DG , and its right Sine ...
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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.