Plane and Solid Geometry: Inductive MethodPress of Hudson-Kimberly Publishing Company, 1898 - 406 σελίδες |
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Σελίδα 72
... equivalent , which are not equal . ] State and prove Prop . XL . ( If you fail , consult " hint " below . ) [ Hint . - Superpose A ' B ' C ' D ' on A B C D so that the equal sides and the included s will coincide . Then show that the ...
... equivalent , which are not equal . ] State and prove Prop . XL . ( If you fail , consult " hint " below . ) [ Hint . - Superpose A ' B ' C ' D ' on A B C D so that the equal sides and the included s will coincide . Then show that the ...
Σελίδα 140
... . α H K G D Draw through I and J lines parallel F H and EG H. Also study the 204 . In the above figure prove a ' : a = FE : IE = HE : KE , etc. SIMILAR FIGURES . 205 . When are two figures equivalent 140 PLANE GEOMETRY , BOOK III .
... . α H K G D Draw through I and J lines parallel F H and EG H. Also study the 204 . In the above figure prove a ' : a = FE : IE = HE : KE , etc. SIMILAR FIGURES . 205 . When are two figures equivalent 140 PLANE GEOMETRY , BOOK III .
Σελίδα 141
... equivalent ? equal ? May a square equal a triangle ? a rectangle ? ( 1 ) Equal figures are not only equal in area , but they are similar in form ; as we have learned , they can be made to coin . cide in all their parts . ( 2 ) Equivalent ...
... equivalent ? equal ? May a square equal a triangle ? a rectangle ? ( 1 ) Equal figures are not only equal in area , but they are similar in form ; as we have learned , they can be made to coin . cide in all their parts . ( 2 ) Equivalent ...
Σελίδα 150
... equivalent to a given rectangle ( assuming that the area of a rectangle equals the product of the base by the altitude ) . 156. Construct a square equivalent to a given rt . 150 PLANE GEOMETRY , BOOK III .
... equivalent to a given rectangle ( assuming that the area of a rectangle equals the product of the base by the altitude ) . 156. Construct a square equivalent to a given rt . 150 PLANE GEOMETRY , BOOK III .
Σελίδα 151
... equivalent to a given rt . A. 157. Given the side of a square and one side of an equiv- alent rectangle . Construct the square and the rectangle . Consult the hint if you fail . It is not difficult . Do not give up easily , [ Hint.-I ...
... equivalent to a given rt . A. 157. Given the side of a square and one side of an equiv- alent rectangle . Construct the square and the rectangle . Consult the hint if you fail . It is not difficult . Do not give up easily , [ Hint.-I ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D adjacent angles altitude axiom base bisect bisector call it Prop chord circle circular sector circumference circumscribed coincide Compare cone Construct convex cube cylinder deduction diagonals diameter diedral angles distance divided drawn equilateral equivalent EXERCISES exterior angle face angles feet figure formed frustum Geometry given line given point hint homologous hypotenuse inches inscribed inscribed angle intersection isosceles Join locus measure middle points number of sides parallel parallelogram parallelopiped Pass a plane pentagon perimeter perpendicular polyedron prism produced proof proportion PROPOSITION prove Prop pupil pyramid quadrilateral radii radius ratio rectangle regular polygon rhombus right angles segments solid sphere spherical polygon spherical triangle square straight angle straight line supplementary angles Suppose surface tangent tetraedron theorem trapezoid triangular prism triedral truth unequal vertex vertices volume Write Prop
Δημοφιλή αποσπάσματα
Σελίδα 231 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 388 - Measures of Length 10 millimeters (mm.) = 1 centimeter (cm.) 10 centimeters = 1 decimeter (dm.) 10 decimeters = 1 meter (m.) 10 meters = 1 dekameter (Dm.) 10 dekameters = 1 hektometer (Hm.) 10 hektometers = 1 kilometer (Km.) 10 kilometers = 1 myriameter (Mm.) Measures of Surface 100 sq.
Σελίδα 126 - Proposition 7. 289. ff four quantities are in proportion, they are in proportion by composition and division; that is, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 391 - Square Measure 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30| square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) Cubic Measure 1728 cubic inches (cu.
Σελίδα 33 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center. The curve which bounds the circle is called the circumference Any portion of the circumference is called an arc.
Σελίδα 20 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 233 - Prove that the area of a triangle is equal to half the product of its perimeter by the radius of the inscribed circle.
Σελίδα 390 - Length 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 5| yards, or 16| feet = 1 rod (rd.) 320 rods, or 5280 feet = 1 mile (mi.) Square Measure 144 square inches (sq.
Σελίδα 308 - If a pyramid is cut by a plane parallel to its base, the...
Σελίδα 391 - CUBIC MEASURE 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 128 cubic feet = 1 cord (cd...