Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
Results 1-5 of 18
Page 11
... Suppose at an infinite Distance be removed the Point , or Eye D ; Then will the Angle D AB , differ infinitely little from a right one : Confequently the Rays DA , DB , will differ infinitely little from E A , FB , the two Parallel Rays ...
... Suppose at an infinite Distance be removed the Point , or Eye D ; Then will the Angle D AB , differ infinitely little from a right one : Confequently the Rays DA , DB , will differ infinitely little from E A , FB , the two Parallel Rays ...
Page 15
... Diagram or Demonstration . THEOREM IX . A Circle oblique to the Plane of the Projection , is projected into an Ellipfis on the faid Plane . Demon- Suppose the Circle Demonftration . CBDE inter- fect the Plane Orthographic Projection . 15.
... Diagram or Demonstration . THEOREM IX . A Circle oblique to the Plane of the Projection , is projected into an Ellipfis on the faid Plane . Demon- Suppose the Circle Demonftration . CBDE inter- fect the Plane Orthographic Projection . 15.
Page 16
Benjamin Martin. Suppose the Circle Demonftration . CBDE inter- fect the Plane of the Projecti on , with its Di- ameter CAD ; To which draw the Diameter BAE . F P M G 1 at Right Angles . And let the Circle , by the Perpendiculars BF , NI ...
Benjamin Martin. Suppose the Circle Demonftration . CBDE inter- fect the Plane of the Projecti on , with its Di- ameter CAD ; To which draw the Diameter BAE . F P M G 1 at Right Angles . And let the Circle , by the Perpendiculars BF , NI ...
Page 30
... Suppose the com- mon Section of the Plane and Circle be Ċ D. The Eye placed in E. The Points to be projected A , B ; draw the Rays E A , Eb , E B C a ' tis evident the Point A is , by this means , projected in a , and the Point B will ...
... Suppose the com- mon Section of the Plane and Circle be Ċ D. The Eye placed in E. The Points to be projected A , B ; draw the Rays E A , Eb , E B C a ' tis evident the Point A is , by this means , projected in a , and the Point B will ...
Page 44
... with the Primitive Circle . Practice , Practice . Suppose the Angle EAG = 58 ° , 44 Problems of the Stereographic Projection . To draw a Great Circle through any given Point, fo as to contain any given Angle with the Pri- mitive.
... with the Primitive Circle . Practice , Practice . Suppose the Angle EAG = 58 ° , 44 Problems of the Stereographic Projection . To draw a Great Circle through any given Point, fo as to contain any given Angle with the Pri- mitive.
Contents
1 | |
2 | |
19 | |
25 | |
43 | |
49 | |
55 | |
103 | |
240 | |
246 | |
252 | |
258 | |
264 | |
275 | |
281 | |
294 | |
112 | |
124 | |
131 | |
138 | |
161 | |
166 | |
200 | |
208 | |
213 | |
221 | |
234 | |
297 | |
305 | |
316 | |
322 | |
325 | |
334 | |
341 | |
347 | |
353 | |
359 | |
366 | |
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.