Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Αποτελέσματα 1 - 5 από τα 47.
Σελίδα 37
... proportional quantities , the last is called a fourth proportional to the other three , taken in order . Since A C B ̄D ' it is obvious that if A is greater than B , C must be greater than D ; if equal , equal ; and if less , less ...
... proportional quantities , the last is called a fourth proportional to the other three , taken in order . Since A C B ̄D ' it is obvious that if A is greater than B , C must be greater than D ; if equal , equal ; and if less , less ...
Σελίδα 38
... proportional quantities , so that A : B :: C : D ; then will AxD - BXC . For , since the four quantities are proportional , A C B D Multiplying each of these equal quantities by B ( Axiom 1 ) . we obtain A : BXC D Multiplying each of ...
... proportional quantities , so that A : B :: C : D ; then will AxD - BXC . For , since the four quantities are proportional , A C B D Multiplying each of these equal quantities by B ( Axiom 1 ) . we obtain A : BXC D Multiplying each of ...
Σελίδα 39
... proportional , they are also proportion- al when taken alternately . Let A , B , C , D be the numerical representatives of four proportional quantities , so that A : B :: C : D ; then will For , since by Prop . I. , And , since by Prop ...
... proportional , they are also proportion- al when taken alternately . Let A , B , C , D be the numerical representatives of four proportional quantities , so that A : B :: C : D ; then will For , since by Prop . I. , And , since by Prop ...
Σελίδα 40
... proportional , they are also proportion- al when taken inversely . Let then will For , since by Prop . I. , or , therefore , by Prop . II . , A : B :: C : D ; B : A :: D : C. A : B :: C : D , AXD = BXC , BXC = AXD ; B : A :: D : C ...
... proportional , they are also proportion- al when taken inversely . Let then will For , since by Prop . I. , or , therefore , by Prop . II . , A : B :: C : D ; B : A :: D : C. A : B :: C : D , AXD = BXC , BXC = AXD ; B : A :: D : C ...
Σελίδα 41
... proportional , they are also proportion al by division . A : B :: C : D ; A - B : A :: C - D : C. A : B :: C : D , BXC = AxD . Subtract each of these equals from AXC ; Let then will For , since by Prop . I. , then or , AXC - BXC = A × C ...
... proportional , they are also proportion al by division . A : B :: C : D ; A - B : A :: C - D : C. A : B :: C : D , BXC = AxD . Subtract each of these equals from AXC ; Let then will For , since by Prop . I. , then or , AXC - BXC = A × C ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.
Σελίδα 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Σελίδα 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Σελίδα 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Σελίδα 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.