Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα v
... Limits . The changes are not sufficient to prevent the simulta- neous use of the old and new editions in the class ; still they are very important , and have been made after the most careful and prolonged consideration . I have to ...
... Limits . The changes are not sufficient to prevent the simulta- neous use of the old and new editions in the class ; still they are very important , and have been made after the most careful and prolonged consideration . I have to ...
Σελίδα vi
... limit ; if , however , x decrease and approach zero as a limit , the area of the rectangle decreases and approaches zero for a limit . An arith- metical illustration of this truth would be given by multiplying a constant into the ...
... limit ; if , however , x decrease and approach zero as a limit , the area of the rectangle decreases and approaches zero for a limit . An arith- metical illustration of this truth would be given by multiplying a constant into the ...
Σελίδα vii
... LIMITS SUPPLEMENTARY PROPOSITIONS CONSTRUCTIONS . . BOOK III . PROPORTIONAL LINES AND SIMILAR POLYGONS . THEORY OF PROPORTION . PROPORTIONAL LINES SIMILAR POLYGONS . CONSTRUCTIONS PAGE 3 4 6 7 9 10 11 12 13 14 24 37 58 68 86 87 2185 73 ...
... LIMITS SUPPLEMENTARY PROPOSITIONS CONSTRUCTIONS . . BOOK III . PROPORTIONAL LINES AND SIMILAR POLYGONS . THEORY OF PROPORTION . PROPORTIONAL LINES SIMILAR POLYGONS . CONSTRUCTIONS PAGE 3 4 6 7 9 10 11 12 13 14 24 37 58 68 86 87 2185 73 ...
Σελίδα 3
... limits ; and of these lines as having points for their extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can ...
... limits ; and of these lines as having points for their extremities or limits . A Solid , as the term is used in Geometry , is a limited por- tion of space . After we acquire a clear notion of surfaces as boundaries of solids , we can ...
Σελίδα 5
... limits ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines ...
... limits ( extremities ) of lines are points . The limits ( boundaries ) of surfaces are lines . The limits ( boundaries ) of solids are surfaces . 7. DEF . Extension is also called Magnitude . When reference is had to extent , lines ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 202 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 146 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.