Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 41
... pendicular to FG ; then will this line be also perpendic- ular to both the lines AB , CD , ( Prop . xvII , Cor . ) and consequently the two lines AB , CD are parallels , ( Prop . XVIII , Cor . ) PROPOSITION XXII . THECREM . If two ...
... pendicular to FG ; then will this line be also perpendic- ular to both the lines AB , CD , ( Prop . xvII , Cor . ) and consequently the two lines AB , CD are parallels , ( Prop . XVIII , Cor . ) PROPOSITION XXII . THECREM . If two ...
Σελίδα 45
... pendicular AB be less than AC , and AC less than AD . D A B For , the angle B being right , the angle C must be acute , ( Prop . vI , ) and therefore less than the angle B ; but the less side of a triangle is situated opposite the less ...
... pendicular AB be less than AC , and AC less than AD . D A B For , the angle B being right , the angle C must be acute , ( Prop . vI , ) and therefore less than the angle B ; but the less side of a triangle is situated opposite the less ...
Σελίδα 68
... pendicular from the obtuse angle . Let ABC be a triangle , obtuse- angled at B , and CD perpendicular to AB ; then will the square of AC be greater than the squares of AB and BC , by twice the rectangle of B D AB and BD ; that is , AC2 ...
... pendicular from the obtuse angle . Let ABC be a triangle , obtuse- angled at B , and CD perpendicular to AB ; then will the square of AC be greater than the squares of AB and BC , by twice the rectangle of B D AB and BD ; that is , AC2 ...
Σελίδα 82
... pendicular to AB it is shorter than the oblique line CF , ( B. I , Prop . xxvi , Cor . ) Hence , the point F is without the circle ; and the same may be shown of any other point of the line AB , except the point D. Consequently the line ...
... pendicular to AB it is shorter than the oblique line CF , ( B. I , Prop . xxvi , Cor . ) Hence , the point F is without the circle ; and the same may be shown of any other point of the line AB , except the point D. Consequently the line ...
Σελίδα 83
... pendicular to AB , ( B. I , Prop . xxvI . ) Cor . 1. Hence , conversely , a line drawn perpendicular to a tangent at the point of contact , passes through the centre of the circle . Cor . 2. If two circumferences touch each other either ...
... pendicular to AB , ( B. I , Prop . xxvI . ) Cor . 1. Hence , conversely , a line drawn perpendicular to a tangent at the point of contact , passes through the centre of the circle . Cor . 2. If two circumferences touch each other either ...
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Elements of Geometry With Practical Applications George R Perkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Δημοφιλή αποσπάσματα
Σελίδα 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Σελίδα 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Σελίδα 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Σελίδα 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Σελίδα 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Σελίδα 120 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 18 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Σελίδα 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.