Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
Results 1-5 of 100
Page vii
... Cafes thereof ; the Method of Solving them by letting fall a Perpendicular ; and Rules for folving all kind of Ambiguities attending them Chap . XIX . 166 Method of folving Oblique Spherical Triangles without a Perpendicular with a ...
... Cafes thereof ; the Method of Solving them by letting fall a Perpendicular ; and Rules for folving all kind of Ambiguities attending them Chap . XIX . 166 Method of folving Oblique Spherical Triangles without a Perpendicular with a ...
Page 42
... Cafes ; Cafe 1. Of the Primitive Circle AF BD ; By Definition IX , its Pole will be in the Center C. Cafe 2. Of a Right Cir- cle , as AB , Set off 90 Degrees from A , or B , each way to the Points E , and D , and thofe Points will be ...
... Cafes ; Cafe 1. Of the Primitive Circle AF BD ; By Definition IX , its Pole will be in the Center C. Cafe 2. Of a Right Cir- cle , as AB , Set off 90 Degrees from A , or B , each way to the Points E , and D , and thofe Points will be ...
Page 43
... Cafe 1. When the An- gle is at the Center of the Primitive C. Let there be made the Angle BCF = 40 ° ; take the Chord of 40 , and fet from B to F , and draw the Line C F ; then is the Angle BCF , of the juft Quantity required . E IC B Cafe ...
... Cafe 1. When the An- gle is at the Center of the Primitive C. Let there be made the Angle BCF = 40 ° ; take the Chord of 40 , and fet from B to F , and draw the Line C F ; then is the Angle BCF , of the juft Quantity required . E IC B Cafe ...
Page 44
... Cafe 3. When the Angle is in the Primitive , but not in the Center , or Periphery ; as at A , Comprehended by the ... Cafe 4. When the Angle A 52 ° 30 ′ . is contained under the Arches of two Oblique Circles HA , and KA ; let it be ...
... Cafe 3. When the Angle is in the Primitive , but not in the Center , or Periphery ; as at A , Comprehended by the ... Cafe 4. When the Angle A 52 ° 30 ′ . is contained under the Arches of two Oblique Circles HA , and KA ; let it be ...
Page 46
... Cafes . Cafe 1. When the Angle is at the Center of the Pri- mitive C , As the Angle BCH ; Take the Arch B H , and and on the Line of Chords you will find it 46 Problems of the Stereographic Projection . To measure any Spherical Angle.
... Cafes . Cafe 1. When the Angle is at the Center of the Pri- mitive C , As the Angle BCH ; Take the Arch B H , and and on the Line of Chords you will find it 46 Problems of the Stereographic Projection . To measure any Spherical Angle.
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.