Elements of Geometry: With Practical Applications, for the Use of Schools |
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Page vi
... Proportions 24 Degrees , minutes , & c . 7 Proportional lines 26 Angles and their measure 7 Similar triangles 30 Right angles , acute angles , obtuse Mean Proportional 31 angles 9 Quadrilaterals 32 Properties of perpendiculars 10 ...
... Proportions 24 Degrees , minutes , & c . 7 Proportional lines 26 Angles and their measure 7 Similar triangles 30 Right angles , acute angles , obtuse Mean Proportional 31 angles 9 Quadrilaterals 32 Properties of perpendiculars 10 ...
Page viii
... proportion , as presented by Euclid , of whom we are next to speak . About 300 years before Christ , Ptolemy Lagus founded a school of philosophy at Alexandria , in which Mathemat- ics was cultivated before every thing else . It was ...
... proportion , as presented by Euclid , of whom we are next to speak . About 300 years before Christ , Ptolemy Lagus founded a school of philosophy at Alexandria , in which Mathemat- ics was cultivated before every thing else . It was ...
Page xv
... proportion geometrically , Whereas in modern systems , these laws are supposed to have been previously demon- strated by the help of Algebra . The moderns also derive great advantage , in every part of geometry , from the use of ...
... proportion geometrically , Whereas in modern systems , these laws are supposed to have been previously demon- strated by the help of Algebra . The moderns also derive great advantage , in every part of geometry , from the use of ...
Page 24
... proportion . Hence the phrase geometrical pro- portion . To explain the nature and laws of proportion be- longs to arithmetic and algebra . We shall not therefore enter into a particular analysis of them here . But for the sake of those ...
... proportion . Hence the phrase geometrical pro- portion . To explain the nature and laws of proportion be- longs to arithmetic and algebra . We shall not therefore enter into a particular analysis of them here . But for the sake of those ...
Page 25
... proportion 2 : 4 :: 4 : 8 , we say 4 is a mean proportion- al between 2 and 8. If more than two equal ratios are written after one another , they form a continued proportion . Thus 69 10 : 15 :: 8 : 12 is a continued proportion . 63. In ...
... proportion 2 : 4 :: 4 : 8 , we say 4 is a mean proportion- al between 2 and 8. If more than two equal ratios are written after one another , they form a continued proportion . Thus 69 10 : 15 :: 8 : 12 is a continued proportion . 63. In ...
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Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker No preview available - 2023 |
Elements of Geometry: With Practical Applications, for the Use of Schools Timothy Walker No preview available - 2019 |
Common terms and phrases
A B C D A B fig adjacent angles axis B A C base and altitude base multiplied bisect called centre chord circ circumference coincide convex surface cube cylinder D E F demonstrated diameter divided draw equally distant equivalent found by multiplying frustum geometry given line gles height Hence homologous sides hundredths inches infinite number infinitely small inscribed angles inscribed circle inscribed sphere intersection line A B line drawn linear unit mean proportional method of Exhaustions number of sides parallel sides perimeter perpendicular polyedrons preceding proposition proved pyramid radii radius ratio regular polygon rence right angle right parallelogram right parallelopiped right triangle semicircumference similar triangles solid angles sphere square feet straight line Suppose tangent tion trapezoid triangles A B C triangles are equal triangular prism vertex vertices
Popular passages
Page 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...
Page xiv - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Page 30 - 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'.
Page xiv - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 25 - In any proportion, the product of the means is equal to the product of the extremes.
Page 38 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 25 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Page xiv - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Page 42 - The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases.
Page 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 lesi than two right angles...