Spherical trigonometryJ. Noon, 1736 |
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Página 4
... Bafe AV . 2. The Perpen- dicular AP . 3. The Complement of the Hypothe- nufe VP , ( viz . the Arch VB . ) 4. The Complement of the Angle at the Bafe V 5. The Complement of the Angle at the perpendicular P ; ( viz . the Arch CB ...
... Bafe AV . 2. The Perpen- dicular AP . 3. The Complement of the Hypothe- nufe VP , ( viz . the Arch VB . ) 4. The Complement of the Angle at the Bafe V 5. The Complement of the Angle at the perpendicular P ; ( viz . the Arch CB ...
Página 86
... Bafe B A , or B H , then the Sines of the Hypo- thenuses , fhall be proportional to the Sines of the Per- pendicular Arches . For the Right Lines Demonftration . being Perpendicular to the fame Plane are parallel . Alfo the Lines ...
... Bafe B A , or B H , then the Sines of the Hypo- thenuses , fhall be proportional to the Sines of the Per- pendicular Arches . For the Right Lines Demonftration . being Perpendicular to the fame Plane are parallel . Alfo the Lines ...
Página 87
... Bafe B is to the Sine of the Vertical Angle A CB :: fo is the Co - fine of the Perpendicular AC : to the Radius . Demonftration . Produce the Sides till the Arches AB , BC , CA , BE , BF , CI , CH , be Quadrants ; and from the Poles B ...
... Bafe B is to the Sine of the Vertical Angle A CB :: fo is the Co - fine of the Perpendicular AC : to the Radius . Demonftration . Produce the Sides till the Arches AB , BC , CA , BE , BF , CI , CH , be Quadrants ; and from the Poles B ...
Página 88
... Bafe ) G , CF ; CA = HD , D C. HIC DC F , I , and F , C ; BA , is less than a Quadrant ; ' twill be , s DF : s HI :: That is , as the Co - fine of the Angle is to the Sine of the Vertical Angle fo is the Co - fine of the Perpendicular ...
... Bafe ) G , CF ; CA = HD , D C. HIC DC F , I , and F , C ; BA , is less than a Quadrant ; ' twill be , s DF : s HI :: That is , as the Co - fine of the Angle is to the Sine of the Vertical Angle fo is the Co - fine of the Perpendicular ...
Página 91
... Bafe B D. Demonftration . By Theorem 27 , we have sBA : RtAC : tB ; and by the fame inverfely RsDA :: t D : t AC . Then it will be , by Equality of perturbate Ratio , SBA : SDA :: t D : t B. Q. E. D. See Euclid 5. Prop . 23 . THEOREM ...
... Bafe B D. Demonftration . By Theorem 27 , we have sBA : RtAC : tB ; and by the fame inverfely RsDA :: t D : t AC . Then it will be , by Equality of perturbate Ratio , SBA : SDA :: t D : t B. Q. E. D. See Euclid 5. Prop . 23 . THEOREM ...
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Términos y frases comunes
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
Pasajes populares
Página 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...
Página 185 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 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.
Página 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.
Página 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.
Página 241 - It commences in the morning and ends in the evening, when the sun is 18° below the horizon.
Página 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.
Página 365 - Dialogue, adapted purpofely to the Capacities of the Youth of both Sexes ; and adorned and illuftrated with variety of Copper- Plates.
Página 75 - Side *»» is the Supplement of the Angle H, and the Angle E of the Side G D.
Página 205 - Superficies to M ; And, as two right Angles are to F, So is half the fpherical Superficies to K.