Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
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Page 17
... Quantity when projected , as Radius to the Co - fine of the Inclina- tion of that Right Line to the Plane of the Projection . VOL . II ... D Demon- Demonftration . Let the given Right Line be DC , Orthographic Projection . 17.
... Quantity when projected , as Radius to the Co - fine of the Inclina- tion of that Right Line to the Plane of the Projection . VOL . II ... D Demon- Demonftration . Let the given Right Line be DC , Orthographic Projection . 17.
Page 18
... 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 D E , are all evidently projected into the right ...
... 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 D E , are all evidently projected into the right ...
Page 19
... Radius CD , : to the Co - fine of the Inclination CF ; :: fo is the Area of the Quadrant C G B , : to the Area of its Projection C F H. And fo is the Area of the whole Circle to its Pro- jection . 2 , E. D. CHA P. III . Problems of the ...
... Radius CD , : to the Co - fine of the Inclination CF ; :: fo is the Area of the Quadrant C G B , : to the Area of its Projection C F H. And fo is the Area of the whole Circle to its Pro- jection . 2 , E. D. CHA P. III . Problems of the ...
Page 25
... Radius , will reach to Cancer and Capricorn , vs : And thus is the Ecliptic divided as required . Q2 . E. F. PROBLEM VII . To annex the Calendar to the Orthographical Pro- jection , or Analemma . See the following Scheme . Practice ...
... Radius , will reach to Cancer and Capricorn , vs : And thus is the Ecliptic divided as required . Q2 . E. F. PROBLEM VII . To annex the Calendar to the Orthographical Pro- jection , or Analemma . See the following Scheme . Practice ...
Page 35
... Radius E C , defcribe the Arch CH ; alfo draw the Line CF. E H N M A G BL By Theor . 3 , the Arch D F will be projected into CG , K which is the Tangent of the Angle CEG ; But ( by the Elements ) the faid Angle CEG DCF , and of ...
... Radius E C , defcribe the Arch CH ; alfo draw the Line CF. E H N M A G BL By Theor . 3 , the Arch D F will be projected into CG , K which is the Tangent of the Angle CEG ; But ( by the Elements ) the faid Angle CEG DCF , and of ...
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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.