Elements of Geometry: With Practical Applications, for the Use of Schools |
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Page viii
... square of the hypothenuse of a right - angled triangle is equal to the sum of the squares of the other two sides . To express his joy and grati- tude for this great discovery , we are told that he sacrificed one hundred oxen to the ...
... square of the hypothenuse of a right - angled triangle is equal to the sum of the squares of the other two sides . To express his joy and grati- tude for this great discovery , we are told that he sacrificed one hundred oxen to the ...
Page x
... square of the hypothenuse , the bride , and the converse of it the bride's sister . Rome never had any distinguished geometers . Cicero professes a high esteem for Mathematics , but did not write upon the subject . The Chinese have ...
... square of the hypothenuse , the bride , and the converse of it the bride's sister . Rome never had any distinguished geometers . Cicero professes a high esteem for Mathematics , but did not write upon the subject . The Chinese have ...
Page 32
... square , and the oblong or rectan F53 gle . The square has all its sides equal ( fig . 53 ) . The F54 oblong has only its opposite sides equal ( fig . 54. ) Oblique • parallelograms have none of their angles right angles . 32 32 ...
... square , and the oblong or rectan F53 gle . The square has all its sides equal ( fig . 53 ) . The F54 oblong has only its opposite sides equal ( fig . 54. ) Oblique • parallelograms have none of their angles right angles . 32 32 ...
Page 33
... square are regular polygons . Irregular polygons are such as do not possess both these properties . Similar polygons are those which have their angles equal , each to each , and their homologous sides proportional . ELEMENTS OF GEOMETRY ...
... square are regular polygons . Irregular polygons are such as do not possess both these properties . Similar polygons are those which have their angles equal , each to each , and their homologous sides proportional . ELEMENTS OF GEOMETRY ...
Page 36
... square . Hav- ing a given circle to inscribe a square . Let the given cir- F60 cle be A B C D ( fig . 60 ) . Draw two diameters perpen- dicular to each other , and join their extremities by chords . A B C D is a square ( 83 ) , because ...
... square . Hav- ing a given circle to inscribe a square . Let the given cir- F60 cle be A B C D ( fig . 60 ) . Draw two diameters perpen- dicular to each other , and join their extremities by chords . A B C D is a square ( 83 ) , because ...
Other editions - View all
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...