Elements of GeometryGinn, Heath, & Company, 1879 - 250 σελίδες |
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Σελίδα 93
... means that an angle at the centre is such part of the angular magnitude about that point ( four right angles ) as its intercepted arc is of the whole circumference . A circumference is divided into 360 equal arcs , and each arc is ...
... means that an angle at the centre is such part of the angular magnitude about that point ( four right angles ) as its intercepted arc is of the whole circumference . A circumference is divided into 360 equal arcs , and each arc is ...
Σελίδα 128
... The Extremes in a proportion are the first and fourth terms . 250. The Means in a proportion are the second and third terms . 251. DEF . In the proportion ab :: cd ; PROPORTIONAL LINES AND SIMILAR POLYGONS THEORY OF PROPORTION.
... The Extremes in a proportion are the first and fourth terms . 250. The Means in a proportion are the second and third terms . 251. DEF . In the proportion ab :: cd ; PROPORTIONAL LINES AND SIMILAR POLYGONS THEORY OF PROPORTION.
Σελίδα 129
... Mean Proportional between a and c . 254. DEF . Four quantities are Reciprocally Proportional when the first is to ... means , or the extremes , are made to exchange places . Thus in the proportion we have either a b c d , a : c :: bd ...
... Mean Proportional between a and c . 254. DEF . Four quantities are Reciprocally Proportional when the first is to ... means , or the extremes , are made to exchange places . Thus in the proportion we have either a b c d , a : c :: bd ...
Σελίδα 130
... 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 .
... 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 .
Σελίδα 131
... mean proportional between two quantities is equal to the square root of their product . In the proportion a bbc , b2 = a c , ( the product of the extremes is equal to the product of the means ) . Whence , extracting the square root , b ...
... mean proportional between two quantities is equal to the square root of their product . In the proportion a bbc , b2 = a c , ( the product of the extremes is equal to the product of the means ) . Whence , extracting the square root , b ...
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.