Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Σελίδα 44
... radius of a circle is a straight line drawn from the center to the circumference . A diameter of a circle is a straight line passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle ...
... radius of a circle is a straight line drawn from the center to the circumference . A diameter of a circle is a straight line passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle ...
Σελίδα 46
... radius CD will coincide with the radius GH , and the point D with the point H. Therefore , the arc AID must coincide with the arc EMH , and be equal to it . Hence , in equal circles , & c . PROPOSITION IV . THEOREM . In equal circles ...
... radius CD will coincide with the radius GH , and the point D with the point H. Therefore , the arc AID must coincide with the arc EMH , and be equal to it . Hence , in equal circles , & c . PROPOSITION IV . THEOREM . In equal circles ...
Σελίδα 48
... radius CE , per- pendicular to the chord AB , divides the arc subtended by this chord , into two equal parts in the point E. Therefore , the radius , & c . Scholium . The center C , the middle point D of the chord AB , and the middle ...
... radius CE , per- pendicular to the chord AB , divides the arc subtended by this chord , into two equal parts in the point E. Therefore , the radius , & c . Scholium . The center C , the middle point D of the chord AB , and the middle ...
Σελίδα 49
... radius FA will 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 ...
... radius FA will 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 ...
Σελίδα 50
... radius CF is perpendicular to the chord AB , it bisects it ( Prop . VI . ) . Hence AF is the 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 ...
... radius CF is perpendicular to the chord AB , it bisects it ( Prop . VI . ) . Hence AF is the 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 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle ACB angle BAC base bisected called chord circle circumference coincide College common cone consequently construct contained convex surface curve described diagonals diameter difference distance divided draw drawn ellipse equal equivalent extremities faces fall figure foci formed four frustum given greater half hence hyperbola included inscribed intersect join less Loomis major axis manner Mathematics mean measured meet multiplied opposite ordinate parallel parallelogram parallelopiped pass perpendicular plane plane MN polygon prism PROBLEM Professor Prop proportional PROPOSITION proved pyramid radii radius ratio reason rectangle regular represent right angles Scholium segment sides similar sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole
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.