Spherical trigonometryJ. Noon, 1736 |
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Página 38
... gives the Center O , of the Projection of the leffer Circle E e F : Draw the Lines QE , E O , Eƒ ; The Right angled Triangle e E f , is divided into two fimilar Triangles e E N , and Nf E , by the Diameter E F Therefore the Angle e EN ...
... gives the Center O , of the Projection of the leffer Circle E e F : Draw the Lines QE , E O , Eƒ ; The Right angled Triangle e E f , is divided into two fimilar Triangles e E N , and Nf E , by the Diameter E F Therefore the Angle e EN ...
Página 43
... give the Pole required . Note , In all thefe Cafes , the Poles of leffer parallel Circles are the fame . PROBLEM II . To describe , or lay down , any Spherical Angle . Practice . In this Problem are four Cafes . Cafe 1. When the An- gle ...
... give the Pole required . Note , In all thefe Cafes , the Poles of leffer parallel Circles are the fame . PROBLEM II . To describe , or lay down , any Spherical Angle . Practice . In this Problem are four Cafes . Cafe 1. When the An- gle ...
Página 47
... give the Angle AED = 44 ° 30 ' ; and thus the Arch d F , will give the Angle DEC = 45 ° 30 ' . Cafe 3. When the Angle is neither in the Center , nor Periphery of the Primitive ; but at P , Thus ; let the Angle to be measured be BP2 ...
... give the Angle AED = 44 ° 30 ' ; and thus the Arch d F , will give the Angle DEC = 45 ° 30 ' . Cafe 3. When the Angle is neither in the Center , nor Periphery of the Primitive ; but at P , Thus ; let the Angle to be measured be BP2 ...
Página 48
... gives the Angle BAD = 35o ; as was required . PROBLEM VI . To lay off any Number of Degrees on any Great Circle . Practice . In this Problem are three Cafes . Cafe 1. To divide the Pri- mitive A E B C this is done by a Line of Chords ...
... gives the Angle BAD = 35o ; as was required . PROBLEM VI . To lay off any Number of Degrees on any Great Circle . Practice . In this Problem are three Cafes . Cafe 1. To divide the Pri- mitive A E B C this is done by a Line of Chords ...
Página 54
... gives the Points of Interfection therewith , and the Secant Complement fet from thofe Points of In- terfection ( or the Tangent Complement fet from the Center E ) upon the Equinoctial , extended when there is occafion , will find the ...
... gives the Points of Interfection therewith , and the Secant Complement fet from thofe Points of In- terfection ( or the Tangent Complement fet from the Center E ) upon the Equinoctial , extended when there is occafion , will find the ...
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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.