Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Σελίδα 44
... passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle are equal ; all the diameters are equal also , and each double of the radius . 3. An arc of a circle is any part of the ...
... passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle are equal ; all the diameters are equal also , and each double of the radius . 3. An arc of a circle is any part of the ...
Σελίδα 48
... passes through two of these points , will necessari- y pass through the third , and be perpendicular to the chord . Also , the perpendicular at the middle of a chord passes through the center of the circle , and through the middle of ...
... passes through two of these points , will necessari- y pass through the third , and be perpendicular to the chord . Also , the perpendicular at the middle of a chord passes through the center of the circle , and through the middle of ...
Σελίδα 49
... pass through the three given points A , B , C. A Secondly . No other circumference can pass through the same points . For , if there were a second , its center could not be out of the line DF , for then it would be unequally dis- tant ...
... pass through the three given points A , B , C. A Secondly . No other circumference can pass through the same points . For , if there were a second , its center could not be out of the line DF , for then it would be unequally dis- tant ...
Σελίδα 52
... pass through C and D , the centers of the two circles ( Prop . VI . , Schol . ) . But only one straight line can be drawn through two given points ; therefore , the straight line which passes through the centers , will bisect the common ...
... pass through C and D , the centers of the two circles ( Prop . VI . , Schol . ) . But only one straight line can be drawn through two given points ; therefore , the straight line which passes through the centers , will bisect the common ...
Σελίδα 89
... pass through three given points A , B , C ; and also , a circle may be described about a triangle . PROBLEM XIV . Through a given point , to draw a tangent to a given circle First . Let the given point A be without the circle BDE ; it ...
... pass through three given points A , B , C ; and also , a circle may be described about a triangle . PROBLEM XIV . Through a given point , to draw a tangent to a given circle First . Let the given point A be without the circle BDE ; it ...
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.