Spherical trigonometryJ. Noon, 1736 - Plane trigonometry |
From inside the book
Results 1-5 of 51
Page 13
... because of the Right Angles AEH , BHE , and the Parallel Lines A B , EH , the Angles E AB , ABH , A B D EF GH are right ones alfo ; fo E A , HB , will touch the Circle in A , and B ; Wherefore all other Lines CF , DG , drawn ...
... because of the Right Angles AEH , BHE , and the Parallel Lines A B , EH , the Angles E AB , ABH , A B D EF GH are right ones alfo ; fo E A , HB , will touch the Circle in A , and B ; Wherefore all other Lines CF , DG , drawn ...
Page 14
... because the given Semicircle Ao D B 77997 is at right Angles to the Plane , by Hypothesis ; fo therefore are the Perpendiculars oq , oq , oq , & c . Hence ( by Theor . 2. ) all the Points 0 , 0 , 0 , 0 , 0 , & c . will be projected into ...
... because the given Semicircle Ao D B 77997 is at right Angles to the Plane , by Hypothesis ; fo therefore are the Perpendiculars oq , oq , oq , & c . Hence ( by Theor . 2. ) all the Points 0 , 0 , 0 , 0 , 0 , & c . will be projected into ...
Page 16
... because NP , and P I , are parallel to BA , and FA ; the Angle BAF = NPI . Therefore the Triangles B E A , NIP , are Similar ; and FA : IP :: BA : NP . Therefore it will be FAq , IPq :: BAq : NPq . But it is BAq : NPq :: CAX AD : CPX PD ...
... because NP , and P I , are parallel to BA , and FA ; the Angle BAF = NPI . Therefore the Triangles B E A , NIP , are Similar ; and FA : IP :: BA : NP . Therefore it will be FAq , IPq :: BAq : NPq . But it is BAq : NPq :: CAX AD : CPX PD ...
Page 17
... because the Circle is oblique to the Plane of the Projection , its Diameter B E is projected into a Line FG lefs than it felf , by Theorem 5. therefore fince FG is lefs than BE DC , it follows the Curve FDGC is an Ellipfis , whofe ...
... because the Circle is oblique to the Plane of the Projection , its Diameter B E is projected into a Line FG lefs than it felf , by Theorem 5. therefore fince FG is lefs than BE DC , it follows the Curve FDGC is an Ellipfis , whofe ...
Page 32
... because the Ray g E b ( in which the highest Point E is feen ) is parallel to the Diameter infinitely ex- tended c d ; and because each Quadrant A E , E B , is projected by the intermediate Rays i , i , i , & c . K , K , K , & c ...
... because the Ray g E b ( in which the highest Point E is feen ) is parallel to the Diameter infinitely ex- tended c d ; and because each Quadrant A E , E B , is projected by the intermediate Rays i , i , i , & c . K , K , K , & c ...
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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.