A Treatise on Plane and Spherical Trigonometry: Including the Construction of the Auxiliary Tables ; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection |
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Page 41
... common , the angles ADC + ACD = ADE + AED = 2ADE . Again , since ADC = ADE + EDC AED + EDC ; and it follows that AED ... SECTION I. 41 ADE and ADC have the angle at A common, ...
... common , the angles ADC + ACD = ADE + AED = 2ADE . Again , since ADC = ADE + EDC AED + EDC ; and it follows that AED ... SECTION I. 41 ADE and ADC have the angle at A common, ...
Page 46
Including the Construction of the Auxiliary Tables ; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection Enoch Lewis. SECTION ... common difference is BC or CD . From the cen- tre O , draw OA , OC ; from B , C , ...
Including the Construction of the Auxiliary Tables ; a Concise Tract on the Conic Sections, and the Principles of Spherical Projection Enoch Lewis. SECTION ... common difference is BC or CD . From the cen- tre O , draw OA , OC ; from B , C , ...
Page 81
... section of this plane and the sperical surface , is greater than any other line in the sphere which is not a ... common section of the planes of two great circles , is a diameter to each of those circles . ( 78 ) Cor . 3. Every great ...
... section of this plane and the sperical surface , is greater than any other line in the sphere which is not a ... common section of the planes of two great circles , is a diameter to each of those circles . ( 78 ) Cor . 3. Every great ...
Page 81
... common section at right angles to CD ; hence the arcs AD , BD , AG and BG , are quadrants . ART . 47. The angle made by two great circles is measured by the arc intercepted between them , at the distance of 90 ° from the angular point ...
... common section at right angles to CD ; hence the arcs AD , BD , AG and BG , are quadrants . ART . 47. The angle made by two great circles is measured by the arc intercepted between them , at the distance of 90 ° from the angular point ...
Page 82
... common section of the planes AEG , AFG , is at right angles to the plane DBC ( 18.2 sup . ) ; wherefore the angles AGE , AGF are right angles ( 1 Def . 2 sup . ) Now , the right angled triangles AGE , AGF , having the perpendicular AG ...
... common section of the planes AEG , AFG , is at right angles to the plane DBC ( 18.2 sup . ) ; wherefore the angles AGE , AGF are right angles ( 1 Def . 2 sup . ) Now , the right angled triangles AGE , AGF , having the perpendicular AG ...
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Common terms and phrases
ABDP adjacent angle angled spherical triangle base bisect C.cos c.sin centre circle Art common section Comp AC cone conical surface consequently construction cosec cosine cotan directrix distance EB² EC² ecliptic ED² ellipse equal equation given angle greater axis Hence hyperbola hypothenuse join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. ART Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore