Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Σελίδα 19
... Data ( singular datum ) . 2. A statement of what is to be proved , called the Conclusion . The term Hypothesis may be used instead of the term data . A supposition made in the course of a demonstration is also called an Hypothesis . 48 ...
... Data ( singular datum ) . 2. A statement of what is to be proved , called the Conclusion . The term Hypothesis may be used instead of the term data . A supposition made in the course of a demonstration is also called an Hypothesis . 48 ...
Σελίδα 24
... Data : Any two adjacent angles , as AOC and COB , whose sum is equal to two right angles . To prove that the exterior sides , 40 A and OB , form one straight line . Proof . AOC + COB = 2 rt . 4 ; ZAOC + 2 COB = a st . L. From data ...
... Data : Any two adjacent angles , as AOC and COB , whose sum is equal to two right angles . To prove that the exterior sides , 40 A and OB , form one straight line . Proof . AOC + COB = 2 rt . 4 ; ZAOC + 2 COB = a st . L. From data ...
Σελίδα 28
... Data : Any straight line , as AB , and any two straight lines each per- A- pendicular to AB , as CD and EF . To prove CD and EF parallel . C E F Proof . Since , by data , both CD and EF are perpendicular to AB , they cannot meet , for ...
... Data : Any straight line , as AB , and any two straight lines each per- A- pendicular to AB , as CD and EF . To prove CD and EF parallel . C E F Proof . Since , by data , both CD and EF are perpendicular to AB , they cannot meet , for ...
Σελίδα 29
... data , then , § 71 , But , data , EF GH . EF AB , GH AB . CD AB , then , § 70 , GH and CD passing through J cannot both be parallel to AB . Hence , the hypothesis that EF is not perpendicular to CD is untenable . Consequently , EF CD ...
... data , then , § 71 , But , data , EF GH . EF AB , GH AB . CD AB , then , § 70 , GH and CD passing through J cannot both be parallel to AB . Hence , the hypothesis that EF is not perpendicular to CD is untenable . Consequently , EF CD ...
Σελίδα 31
... data and conclusion of one become the conclusion and data , respec- tively , of the other , the one is said to be the converse of the other . Thus , the converse of the theorem just proved is , " Two straight lines cut by a transversal ...
... data and conclusion of one become the conclusion and data , respec- tively , of the other , the one is said to be the converse of the other . Thus , the converse of the theorem just proved is , " Two straight lines cut by a transversal ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle cylinder Data diagonals diameter dihedral angles distance divided equal circles equidistant equilateral triangle equivalent exterior angle extremities FGHJK Find the locus frustum given line given point given straight line Hence homologous sides hypotenuse inscribed angle intersecting isosceles trapezoid isosceles triangle measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane polyhedron prism produced Proof prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angle right triangle secant segments sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Σελίδα 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Σελίδα 219 - 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.
Σελίδα 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Σελίδα 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Σελίδα 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Σελίδα 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.