Elements of Geometry and Conic SectionsHarper, 1858 - 234 σελίδες |
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Σελίδα 6
... reasons , both of these rules have been departed from . Throughout Solid Geometry the figures have generally been shaded , which addition , it is hoped , will obviate some of the difficulties of which students frequent- ly complain ...
... reasons , both of these rules have been departed from . Throughout Solid Geometry the figures have generally been shaded , which addition , it is hoped , will obviate some of the difficulties of which students frequent- ly complain ...
Σελίδα 6
... reasons , both of these rules have been departed from . Throughout Solid Geometry the figures have generally been shaded , which addition , it is hoped , will obviate some of the difficulties of which students frequent- ly complain ...
... reasons , both of these rules have been departed from . Throughout Solid Geometry the figures have generally been shaded , which addition , it is hoped , will obviate some of the difficulties of which students frequent- ly complain ...
Σελίδα 19
... reason , BC is less than the sum of AB and AC ; and AC less than the sum of AB and BC Therefore , any two sides , & c . PROPOSITION IX . THEOREM . If , from a point within a triangle , two straight lines are drawn to the extremities of ...
... reason , BC is less than the sum of AB and AC ; and AC less than the sum of AB and BC Therefore , any two sides , & c . PROPOSITION IX . THEOREM . If , from a point within a triangle , two straight lines are drawn to the extremities of ...
Σελίδα 33
... reason , AC is parallel to BD ; hence the quadrilateral ABDC is a par- allelogram . Therefore , if the opposite sides , & c . PROPOSITION XXXI . THEOREM . If two opposite sides of a quadrilateral are equal and par- allel , the other two ...
... reason , AC is parallel to BD ; hence the quadrilateral ABDC is a par- allelogram . Therefore , if the opposite sides , & c . PROPOSITION XXXI . THEOREM . If two opposite sides of a quadrilateral are equal and par- allel , the other two ...
Σελίδα 49
... reason ; therefore , it must be on both the lines DF , FE . But two straight lines can not cut each other in more than one point ; hence only one cir- cumference can pass through three given points . Therefore , through three given ...
... reason ; therefore , it must be on both the lines DF , FE . But two straight lines can not cut each other in more than one point ; hence only one cir- cumference can pass through three given points . Therefore , through three given ...
Άλλες εκδόσεις - Προβολή όλων
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.