Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
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Page 38
... whose Diameter is EF , F A and its Poles are B , and D. Here the Eye is placed in A : Draw the Lines Ae E , A Ff , then fhall the Diameter E F be projected into the Line eƒ ; which bifected , gives the Center O , of the Projection of ...
... whose Diameter is EF , F A and its Poles are B , and D. Here the Eye is placed in A : Draw the Lines Ae E , A Ff , then fhall the Diameter E F be projected into the Line eƒ ; which bifected , gives the Center O , of the Projection of ...
Page 72
... whose Complement PN , or 2 , is 17 ° 26 ' ; and that is the Latitude in which this Reclining Plane will be an Horizontal Dial . 16. Lastly , lay a Ruler from P to a , and it will cut the Primitive in b ; then Th measured on the Chords ...
... whose Complement PN , or 2 , is 17 ° 26 ' ; and that is the Latitude in which this Reclining Plane will be an Horizontal Dial . 16. Lastly , lay a Ruler from P to a , and it will cut the Primitive in b ; then Th measured on the Chords ...
Page 205
... find the Angle B CD . Measure KL on a Line of Half - tangents from 90 downwards , and you will find it to be 769 00 ' , whose Complement 1049 is the Angle required . Cafe Cafe 5 . BD 8 1 42 09 , 30 Triangles by the Stereogr Projection .
... find the Angle B CD . Measure KL on a Line of Half - tangents from 90 downwards , and you will find it to be 769 00 ' , whose Complement 1049 is the Angle required . Cafe Cafe 5 . BD 8 1 42 09 , 30 Triangles by the Stereogr Projection .
Page 249
... - fine of R C 44 ° 06 ′ 9.8562088 So is the Co - fine of PE = 23 ° 29 ′ 9.9624527 To the Co - fine of PC 44 ° 161 VOL . II . 9.8547428 K k Whose Whofe Complement is 45 ° 42 ′ = AC the in various Problems of the Sphere . 249.
... - fine of R C 44 ° 06 ′ 9.8562088 So is the Co - fine of PE = 23 ° 29 ′ 9.9624527 To the Co - fine of PC 44 ° 161 VOL . II . 9.8547428 K k Whose Whofe Complement is 45 ° 42 ′ = AC the in various Problems of the Sphere . 249.
Page 274
... whose Poles are P and S ; 10 2 4 , the Eclip- tic ; HAO , HBO , A 10 12 B F G K E P & c . are the Circles of Pofition ; PFSL , the Ele- vation of the Pole above the Circles of Pofition of the 11th , 9th , 3d , and 5th Houfes , 11th ...
... whose Poles are P and S ; 10 2 4 , the Eclip- tic ; HAO , HBO , A 10 12 B F G K E P & c . are the Circles of Pofition ; PFSL , the Ele- vation of the Pole above the Circles of Pofition of the 11th , 9th , 3d , and 5th Houfes , 11th ...
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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.