Elements of GeometryGinn, Heath, & Company, 1879 - 250 σελίδες |
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Σελίδα vi
... multiplied by 60 give the series 18 , 19.8 , 19.98 , 19.998 , etc. , which evidently approach 20 as a limit ; but the product of 60 into ( the limit of the repetend .333 , etc. ) is also 20 . 33 333 Again , if we multiply 60 into the ...
... multiplied by 60 give the series 18 , 19.8 , 19.98 , 19.998 , etc. , which evidently approach 20 as a limit ; but the product of 60 into ( the limit of the repetend .333 , etc. ) is also 20 . 33 333 Again , if we multiply 60 into the ...
Σελίδα 7
... multiplied , and the result- ing line is called a multiple of the given line . = BC CD , etc. , 3 A B , etc. A B с ... multiply , and divide lines of given length . 21. Since every straight line has the property of direction , it must be ...
... multiplied , and the result- ing line is called a multiple of the given line . = BC CD , etc. , 3 A B , etc. A B с ... multiply , and divide lines of given length . 21. Since every straight line has the property of direction , it must be ...
Σελίδα 14
... multiplied by . divided by . Def . definition . Ax . axiom . Hyp . hypothesis . Cor . corollary . Q. E. D. quod erat demonstran- dum . Q. E. F. quod erat faciendum . Adj . adjacent . Ext . - int . exterior - interior . Alt . - int ...
... multiplied by . divided by . Def . definition . Ax . axiom . Hyp . hypothesis . Cor . corollary . Q. E. D. quod erat demonstran- dum . Q. E. F. quod erat faciendum . Adj . adjacent . Ext . - int . exterior - interior . Alt . - int ...
Σελίδα 90
... Multiply these equations together . Then , xyz = abc terms which contain one or more of the factors v , v ' , v ' , and hence have zero for a limit . .. lim . ( x y z ) - But lim . ( a b c = lim . ( a b c ‡ terms whose limits are zero ) ...
... Multiply these equations together . Then , xyz = abc terms which contain one or more of the factors v , v ' , v ' , and hence have zero for a limit . .. lim . ( x y z ) - But lim . ( a b c = lim . ( a b c ‡ terms whose limits are zero ) ...
Σελίδα 130
... extremes is equal to the product of the means . Let a : b :: c : d . We are to prove ad = bc . Now 816 a = с whence , by multiplying by bd , ad = bc . axt Q. E. D. It is to be observed that the product of two 130 BOOK III . GEOMETRY .
... extremes is equal to the product of the means . Let a : b :: c : d . We are to prove ad = bc . Now 816 a = с whence , by multiplying by bd , ad = bc . axt Q. E. D. It is to be observed that the product of two 130 BOOK III . GEOMETRY .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C AABC AACB ABCD acute adjacent angles alt.-int altitude arc A B base bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure Geometry given circle given line given point given straight line greater homologous sides hypotenuse Iden isosceles triangle Let A B limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular PHILLIPS EXETER ACADEMY plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral quantities radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment shortest side sides of equal similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 144 - 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'.
Σελίδα 38 - 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 134 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 200 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 173 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 159 - In any triangle the product of two sides is equal to the product of the diameter...
Σελίδα 132 - 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 70 - I) is a parallelogram, E and F the middle points of AD and BC respectively ; show that BE and DF will trisect the diagonal A C.
Σελίδα 48 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Σελίδα 81 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.