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 |
From inside the book
Results 1-5 of 35
Page 41
... common , the angles ADC + ACD = ADE + AED : = 2ADE . Again , since ADC = ADE + EDC = AED + EDC ; and AED = ACD + EDC ... 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 AED = ACD + EDC ... SECTION I. 41 ADE and ADC have the angle at A common, ...
Page 43
Including the Construction of the Auxiliary Tables; a Concise Tract on the Conic Sections ... common , and the perpendiculars DG , EG , equal , we have reason , BD = BF ... SECTION I. 43.
Including the Construction of the Auxiliary Tables; a Concise Tract on the Conic Sections ... common , and the perpendiculars DG , EG , equal , we have reason , BD = BF ... SECTION I. 43.
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 , D ...
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 , D ...
Page 78
... 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 80
... 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 ...
Other editions - View all
Common terms and phrases
ABDP 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 drawn 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
Popular passages
Page 32 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 39 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 98 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.
Page 40 - Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining angle ECB will be their half difference.
Page 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 115 - The straight line joining the vertex and the centre of the base is called the axis of the cone.
Page 97 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Page 82 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C
Page 82 - If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal.