Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 páginas |
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Página xii
... difference between the two limits , is reduced to a quantity too small to be estimated . It is then said to be exhausted , and the area of either of the polygons may be taken for the area of the circle . This is the method which ...
... difference between the two limits , is reduced to a quantity too small to be estimated . It is then said to be exhausted , and the area of either of the polygons may be taken for the area of the circle . This is the method which ...
Página 26
... difference between that angle and two right angles . COR . - Equal an- gles have equal complements and equal supple- ments , and the converse . Thus E AC ( fig . 9 ) , is the complement of E A B , and the supplement of E A D. If EA C is ...
... difference between that angle and two right angles . COR . - Equal an- gles have equal complements and equal supple- ments , and the converse . Thus E AC ( fig . 9 ) , is the complement of E A B , and the supplement of E A D. If EA C is ...
Página 35
... difference between IA C and B A C , and must therefore have for its measure the difference between their measures , that is , the difference between half of IGA and half of B G A , which is half of B I. 42. COROLLARY . — All angles ...
... difference between IA C and B A C , and must therefore have for its measure the difference between their measures , that is , the difference between half of IGA and half of B G A , which is half of B I. 42. COROLLARY . — All angles ...
Página 43
... difference of the two first is to that of the two last , as the first is to the third , or as the second is to the fourth . Thus from the proportion 2 : 46 : 12 we have 2 + 4 : 6 + 12 :: 26 and 4-2 : 12- -6 4 12. Apply the test and both ...
... difference of the two first is to that of the two last , as the first is to the third , or as the second is to the fourth . Thus from the proportion 2 : 46 : 12 we have 2 + 4 : 6 + 12 :: 26 and 4-2 : 12- -6 4 12. Apply the test and both ...
Página 45
... difference of the two first terms , and CE the difference of the two last , we have ( 68 ) these two BDCE :: AB : A C BDCE :: AD : A E. Inverting the means ( 65 ) we have these two BD : AB :: CE : AC BD AD :: CE : A E. 71. THEOREM ...
... difference of the two first terms , and CE the difference of the two last , we have ( 68 ) these two BDCE :: AB : A C BDCE :: AD : A E. Inverting the means ( 65 ) we have these two BD : AB :: CE : AC BD AD :: CE : A E. 71. THEOREM ...
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Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker Sin vista previa disponible - 2023 |
Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker Sin vista previa disponible - 2019 |
Términos y frases comunes
A B C D A B fig adjacent angles angles are equal axis B A C base and altitude base multiplied bisect called centre chord circ circumference coincide contain convex surface cube cylinder definition demonstrated diameter divided draw equally distant equivalent found by multiplying frustum geometry given line given square greater half the arc Hence homologous sides hypothenuse inches infinite number infinitely small inscribed angles inscribed circle line A B line drawn linear unit mean proportional number of sides parallel sides parallelopiped perim perpendicular polyedrons preceding proposition proved pyramid radii radius regular polygon right angles right parallelogram right triangle semicircumference similar triangles solid angles sphere square feet straight line suppose tangent THEOREM.-The solidity tion trapezoid triangle A B C triangles are equal triangular prism vertex vertices
Pasajes populares
Página ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Página 48 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Página 63 - The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.
Página ii - ... and also to an Act, entitled, " An Act- supplementary to an Act, entitled, ' An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the limes therein mentioned ;' and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints.
Página xiv - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página xv - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 41 - In any proportion, the product of the means is equal to the product of the extremes.
Página xiv - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Página 42 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Página xiv - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another.