Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 sider |
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Side 5
... chord . The portion of space comprehended between an arc G B and its chord is called a segment . The portion of space E A B comprehended between the two radii E A , A 1 * ELEMENTS OF GEOMETRY .
... chord . The portion of space comprehended between an arc G B and its chord is called a segment . The portion of space E A B comprehended between the two radii E A , A 1 * ELEMENTS OF GEOMETRY .
Side 6
... chords will be equal , and conversely if two chords are equal their arcs will be equal . This proposition , which is ... chord D G be applied to D F , as they are by hypothesis or supposition equal , the point G must fall upon F. Then ...
... chords will be equal , and conversely if two chords are equal their arcs will be equal . This proposition , which is ... chord D G be applied to D F , as they are by hypothesis or supposition equal , the point G must fall upon F. Then ...
Side 7
... chord B C in the compasses , and placing one foot in D move the other round till it cuts D F in F. The arc D F will be equal to B C because their chords are equal ( 13 ) . 15. It often becomes necessary to compare an arc with an entire ...
... chord B C in the compasses , and placing one foot in D move the other round till it cuts D F in F. The arc D F will be equal to B C because their chords are equal ( 13 ) . 15. It often becomes necessary to compare an arc with an entire ...
Side 8
... chords equal ( 14 ) , nor would the degrees by which the arcs are measured , have the same value ( 15 ) . The student will now understand why the value of angles as well as arcs is expressed in degrees , minutes , & c . 18. For the sake ...
... chords equal ( 14 ) , nor would the degrees by which the arcs are measured , have the same value ( 15 ) . The student will now understand why the value of angles as well as arcs is expressed in degrees , minutes , & c . 18. For the sake ...
Side 12
... chord E B = the chord E C. Then ( 13 ) the arc B E - the arc E C , that is , the arc B C is bisected at E. Also the angle A is bisected , for B A E = E A C , having the same measure . 28. —If a perpendicular be erected upon the middle ...
... chord E B = the chord E C. Then ( 13 ) the arc B E - the arc E C , that is , the arc B C is bisected at E. Also the angle A is bisected , for B A E = E A C , having the same measure . 28. —If a perpendicular be erected upon the middle ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side xiv - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Side 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'.
Side xiv - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 25 - In any proportion, the product of the means is equal to the product of the extremes.
Side 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.
Side 25 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Side 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.
Side 42 - The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases.
Side 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...