Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 13
... half of A. The square of the line AB is denoted by AB2 ; its cube by AB3 . The sign indicates a root to be extracted ; thus , 2 de- notes the square root of 2 ; ✓AXB denotes the square root of the product of A and B. N.B. - The first ...
... half of A. The square of the line AB is denoted by AB2 ; its cube by AB3 . The sign indicates a root to be extracted ; thus , 2 de- notes the square root of 2 ; ✓AXB denotes the square root of the product of A and B. N.B. - The first ...
Σελίδα 24
... half of ABF , is shorter than AC , the half of ACF . Therefore , the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC and AE be two oblique lines which meet the line DE at equal distances from the perpendicular ...
... half of ABF , is shorter than AC , the half of ACF . Therefore , the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC and AE be two oblique lines which meet the line DE at equal distances from the perpendicular ...
Σελίδα 25
... half of ACF , is less than AD , the half of ADF ; hence the oblique line which is furthest from the per- pendicular is the longest . Therefore , if from a point , & c . Cor . 1. The perpendicular measures the shortest distance of a ...
... half of ACF , is less than AD , the half of ADF ; hence the oblique line which is furthest from the per- pendicular is the longest . Therefore , if from a point , & c . Cor . 1. The perpendicular measures the shortest distance of a ...
Σελίδα 50
... half of AB ; and , for the same reason , DG is the half of DE . But AB is equal to DE ; therefore AF is equal to DG ( Axiom 7 , B. I. ) . Now , in the right - angled triangles ACF , DCG , the hypothenuse AC 18 equal to the hypothenuse ...
... half of AB ; and , for the same reason , DG is the half of DE . But AB is equal to DE ; therefore AF is equal to DG ( Axiom 7 , B. I. ) . Now , in the right - angled triangles ACF , DCG , the hypothenuse AC 18 equal to the hypothenuse ...
Σελίδα 55
... half of BE . For the same reason , the angle DAE is measured by half the arc DE . Therefore , the whole angle BAD is meas- ured by half the arc BD . Second . Let C , the center of the circle , be without the angle BAD . Draw the di ...
... half of BE . For the same reason , the angle DAE is measured by half the arc DE . Therefore , the whole angle BAD is meas- ured by half the arc BD . Second . Let C , the center of the circle , be without the angle BAD . Draw the di ...
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.