Elements of Geometry: With Practical Applications, for the Use of Schools |
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Page 19
... we shall see hereafter , all figures bounded by straight lines may either be divided into seve- ral triangles , or reduced to one equivalent triangle . 45. Every triangle may be inscribed in a circle- . ELEMENTS OF GEOMETRY . 19 Triangles.
... we shall see hereafter , all figures bounded by straight lines may either be divided into seve- ral triangles , or reduced to one equivalent triangle . 45. Every triangle may be inscribed in a circle- . ELEMENTS OF GEOMETRY . 19 Triangles.
Page 40
... equivalent , which embrace equal quantities of surface . The question then arises , how is this quantity of surface to be estimated ? In other words , how are sur- faces measured and compared ? In measuring and compar- ing lines , ( 7 ) ...
... equivalent , which embrace equal quantities of surface . The question then arises , how is this quantity of surface to be estimated ? In other words , how are sur- faces measured and compared ? In measuring and compar- ing lines , ( 7 ) ...
Page 41
... equivalent to a right parallelogram of the same base and altitude , it will follow that it must have the same measure , namely , its base into its altitude . Accordingly let A B E F ( fig . 66 ) be a right parallelogram , and A BF66 CD ...
... equivalent to a right parallelogram of the same base and altitude , it will follow that it must have the same measure , namely , its base into its altitude . Accordingly let A B E F ( fig . 66 ) be a right parallelogram , and A BF66 CD ...
Page 42
... equivalents will remain . Therefore A B C D = A BEF , and the area of A B C D = A BXB E , this being the meas- ure of ABEF ( 100 ) . - 102. The area of any triangle is equal to half the pro- duct of its base by its altitude- By the ...
... equivalents will remain . Therefore A B C D = A BEF , and the area of A B C D = A BXB E , this being the meas- ure of ABEF ( 100 ) . - 102. The area of any triangle is equal to half the pro- duct of its base by its altitude- By the ...
Page 43
... equivalent to CE D. Why ? Because they have the same base C E and their altitudes are equal , since their vertices F and D are in a line parallel to C E. Consequently , having the same measure , the triangles are equivalent . Then by ...
... equivalent to CE D. Why ? Because they have the same base C E and their altitudes are equal , since their vertices F and D are in a line parallel to C E. Consequently , having the same measure , the triangles are equivalent . Then by ...
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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...