Plane and Solid Geometry: Inductive MethodPress of Hudson-Kimberly Publishing Company, 1898 - 406 σελίδες |
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Σελίδα 5
... equal to a given angle ; ( 2 ) To bisect a given angle , etc. , have not yet been proved to be geometrically true . In Proposition I. he does not know that he has two triangles in which two respective sides and included angles are equal ...
... equal to a given angle ; ( 2 ) To bisect a given angle , etc. , have not yet been proved to be geometrically true . In Proposition I. he does not know that he has two triangles in which two respective sides and included angles are equal ...
Σελίδα 6
... equal D E , D F , and / E D F. To prove : The triangles A B C and D E F equal . III . The Construction , which consists of the drawing of aid lines , superposition of figures , etc. Here the authority for the work should be shown to ...
... equal D E , D F , and / E D F. To prove : The triangles A B C and D E F equal . III . The Construction , which consists of the drawing of aid lines , superposition of figures , etc. Here the authority for the work should be shown to ...
Σελίδα 20
... equal , respectively , to two sides and the included angle of the other , the triangles are equal . What is known , or admitted to be true , about the two triangles above mentioned ? What are we required to prove is true ? Or , if M N ...
... equal , respectively , to two sides and the included angle of the other , the triangles are equal . What is known , or admitted to be true , about the two triangles above mentioned ? What are we required to prove is true ? Or , if M N ...
Σελίδα 21
... equal to the same thing , or equal things , are equal to each other . ( 2 ) If the same operation be performed on equals , the results will be equal . ( 3 ) The whole is greater than any of its parts . ( 4 ) The whole is equal to the ...
... equal to the same thing , or equal things , are equal to each other . ( 2 ) If the same operation be performed on equals , the results will be equal . ( 3 ) The whole is greater than any of its parts . ( 4 ) The whole is equal to the ...
Σελίδα 24
... equal- ity of two figures is to show that when one is superposed upon the other their boundaries coincide , and the figures are con- sequently equal , by Axiom 8 . 17 . Thus - suppose we wish to prove that All straight angles are equal ...
... equal- ity of two figures is to show that when one is superposed upon the other their boundaries coincide , and the figures are con- sequently equal , by Axiom 8 . 17 . Thus - suppose we wish to prove that All straight angles are equal ...
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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...