Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.Sargent, Wilson & Hinkle, 1868 - 420 σελίδες |
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Σελίδα 23
... curve is used for a curved line . 46. A line composed of straight lines , is called BROKEN . A line may be composed of curves , or of both curved and straight parts . THE STRAIGHT LINE . 47. Problem . - A straight line may be made to ...
... curve is used for a curved line . 46. A line composed of straight lines , is called BROKEN . A line may be composed of curves , or of both curved and straight parts . THE STRAIGHT LINE . 47. Problem . - A straight line may be made to ...
Σελίδα 24
... curve BC were to revolve upon the two points B and C as piv- ots , then the straight line con- B C necting these points would remain at rest , and the curve would revolve about it . A straight line about which any thing revolves , is ...
... curve BC were to revolve upon the two points B and C as piv- ots , then the straight line con- B C necting these points would remain at rest , and the curve would revolve about it . A straight line about which any thing revolves , is ...
Σελίδα 26
... curve . Why ? DIVISION OF SUBJECT . 63. By combinations of lines upon a plane , PLANE FIGURES are formed , which may or may not inclose an area . By combinations of lines and surfaces , figures are formed in space , which may or may not ...
... curve . Why ? DIVISION OF SUBJECT . 63. By combinations of lines upon a plane , PLANE FIGURES are formed , which may or may not inclose an area . By combinations of lines and surfaces , figures are formed in space , which may or may not ...
Σελίδα 31
... curve or a broken line is said to be CONCAVE on the side toward the straight line which joins two of its points , and CONVEX to the other side . 79. Theorem . - A broken line which is convex toward another line that unites its extreme ...
... curve or a broken line is said to be CONCAVE on the side toward the straight line which joins two of its points , and CONVEX to the other side . 79. Theorem . - A broken line which is convex toward another line that unites its extreme ...
Σελίδα 32
... curve for the outer line ; also , By letting the inner line consist of two or of four straight lines . 81. A fine thread being tightly stretched , and thus forced to assume that position which is the shortest path between its ends , is ...
... curve for the outer line ; also , By letting the inner line consist of two or of four straight lines . 81. A fine thread being tightly stretched , and thus forced to assume that position which is the shortest path between its ends , is ...
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adjacent angles altitude angles equal apothem axis base bisect chord circle circumference circumscribed coincide cone Corollary Corollary.-The cosine Cotang curved surface cylinder demonstrated diagonals diameter dicular diedral angle distance divided draw equally distant equivalent EXERCISES faces figure formula four right angles frustum functions Geometry given angle given line given point given straight line given triangle greater Hence homologous homologous lines hypotenuse included angle inscribed intersection isosceles join less let fall mantissa measured number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron prism Problem.-Given pyramid quadrilateral radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged slant hight sphere spherical excess spherical polygon spherical triangle square student subtracting symmetrical Tang tangent tetraedrons theorem Theorem.-The triangles are equal triedral trirectangular vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Σελίδα 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Σελίδα 72 - Problem. — To draw a line through a given point parallel to a given line.
Σελίδα 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Σελίδα 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary. — When the radius is unity, the area is expressed by -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Σελίδα 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Σελίδα 260 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Σελίδα 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.