Elements of Plane and Solid GeometryGinn and Heath, 1877 - 398 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 4 7 9 10 11 12 13 • 14 24 37 58 68 73 75 86 87 100 ...
... LIMITS SUPPLEMENTARY PROPOSITIONS CONSTRUCTIONS . BOOK III . PROPORTIONAL LINES AND SIMILAR POLYGONS . THEORY OF PROPORTION PROPORTIONAL LINES SIMILAR POLYGONS . CONSTRUCTIONS PAGE 4 7 9 10 11 12 13 • 14 24 37 58 68 73 75 86 87 100 ...
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
AABC ABCD altitude arc A B axis base and altitude bisect centre circle circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided Draw equal respectively equally distant equilateral equivalent figure frustum Geometry given point greater Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC limit line A B measured by arc middle point mutually equiangular number of sides opposite parallel parallelogram parallelopiped perimeter perpendicular plane MN prism prove pyramid Q. E. D. PROPOSITION radii radius equal ratio rectangles regular polygon right angles right triangle SCHOLIUM segment sides of equal similar polygons slant height sphere spherical angle spherical polygon spherical triangle square subtend surface symmetrical tangent tetrahedron THEOREM third side trihedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 132 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 140 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 206 - In any proportion, the product of the means is equal to the product of the extremes.
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 353 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 179 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 192 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 150 - 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'.