Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is Added a Book on Proportion, with Notes and IllustrationsDurrie and Peck, 1844 - 237 σελίδες |
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Σελίδα 60
... proportional to their angles ; therefore two sectors ACB , DCE , taken in the same circle , or in equal circles , are to each other as the arcs AB , DE , the bases of those sectors . Hence it is evident that the arcs of the circle ...
... proportional to their angles ; therefore two sectors ACB , DCE , taken in the same circle , or in equal circles , are to each other as the arcs AB , DE , the bases of those sectors . Hence it is evident that the arcs of the circle ...
Σελίδα 76
... proportional , because the ratio of 12 4 is equal to 6 : 2 . : 12. Proportion is expressed , either by the sign of equality , ( = ) , or by four points , ( ) placed between the two ratios . Thus the expressions , A C BD ' and A : B ...
... proportional , because the ratio of 12 4 is equal to 6 : 2 . : 12. Proportion is expressed , either by the sign of equality , ( = ) , or by four points , ( ) placed between the two ratios . Thus the expressions , A C BD ' and A : B ...
Σελίδα 81
... proportional , the product of the ex- tremes is equal to the product of the means . If A : B : : CD , then is For , since , ( Def . 11. 3 , ) AD = BC . A C B D Multiply in each by BD , ( Def . 10. 3 , ) AD = BC . Again , 86 : 12 : 9 ...
... proportional , the product of the ex- tremes is equal to the product of the means . If A : B : : CD , then is For , since , ( Def . 11. 3 , ) AD = BC . A C B D Multiply in each by BD , ( Def . 10. 3 , ) AD = BC . Again , 86 : 12 : 9 ...
Σελίδα 82
... and the two factors of the other for the means . PROPOSITION VII . THEOREM . If three magnitudes are proportional , the product of the ex- tremes is equal to the square of the mean . If A : B : : B : C , 82 GEOMETRY .
... and the two factors of the other for the means . PROPOSITION VII . THEOREM . If three magnitudes are proportional , the product of the ex- tremes is equal to the square of the mean . If A : B : : B : C , 82 GEOMETRY .
Σελίδα 83
... proportional between two magnitudes may found by extracting the square root of their product . be Thus , a mean proportional between 12 and 3 , is √12x3 = 6 . PROPOSITION VIII . THEOREM . If four magnitudes be proportional , they will ...
... proportional between two magnitudes may found by extracting the square root of their product . be Thus , a mean proportional between 12 and 3 , is √12x3 = 6 . PROPOSITION VIII . THEOREM . If four magnitudes be proportional , they will ...
Συχνά εμφανιζόμενοι όροι και φράσεις
Abridgment of Day's adjacent angles allel altitude angle ACB angle BAC antecedent base ABCD bisect centre chord circ circle circumference circumscribed polygon common cone consequently convex surface couplets cylinder Day's Algebra diagonal diameter divided draw drawn equal and parallel equal angles equally distant equiangular equilateral triangles equivalent four magnitudes frustum geometry greater half homologous sides hypothenuse hypothesis inscribed polygon interior angles intersection let fall manner mean proportional measured number of sides oblique lines opposite parallelogram pendicular perimeter perpendicular plane angles plane MN polyedron polygon ABCDE President Day prism PROBLEM Prop PROPOSITION XI pyramid SABCDE quadrilateral quantity radii radius ratio rectangle regular polygon respectively equal SABC Scholium Schools and Academies segment similar solid angle sphere square described straight line tangent THEOREM Thomson trapezium triangle ABC triangular prism vertex Yale College
Δημοφιλή αποσπάσματα
Σελίδα 196 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Σελίδα 176 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Σελίδα 125 - AB as a diameter, describe a semicircle : at the extremity of the diameter draw the tangent AD, equal to the side of the square C ; through the point D and the centre O draw the secant DF ; then will DE and DF be the adjacent sides of the rectangle required. For...
Σελίδα 229 - The area of the circle, we infer therefore, is equal to 3.1415926. Some doubt may exist perhaps about the last decimal figure, owing to errors proceeding from the parts omitted ; but the calculation has been carried on with an additional figure, that the final result here given might be absolutely correct even to the last decimal place. Since the...
Σελίδα 118 - B, may be found in the same manner, for it will be the same as a fourth proportional to the three lines A, B, B. PROBLEM IIL To find a mean proportional between two given lines A and B.
Σελίδα 176 - DEF, def, are equivalent; for like reasons, the third exterior prism GHI-K and the second interior prism ghi-d are equivalent; the fourth exterior and the third interior ; and so on, to the last in each series. Hence all the exterior prisms of the pyramid...
Σελίδα 46 - 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 220 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 101 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
Σελίδα 227 - The surface of a regular inscribed polygon, and that of a similar polygon circumscribed, being given ; to find the surfaces of the regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon ; C the centre of the circle. If the chord AM and the tangents AP, BQ, be drawn, AM...