Plane Geometry: A Complete Course in the Elements of the ScienceChristopher Sower Company, 1901 - 266 σελίδες |
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Σελίδα 4
... given " and what is " to be proved , " and also in seeing just where the argument for the proof begins . This difficulty has been obviated by the use of the side headings - Given , To Prove , and Proof . The classification of the ...
... given " and what is " to be proved , " and also in seeing just where the argument for the proof begins . This difficulty has been obviated by the use of the side headings - Given , To Prove , and Proof . The classification of the ...
Σελίδα 10
... given lines . Plato , the " poetical philosopher , " delighted in the science and culti- vated it with great success . He made mathematics the basis of his in- struction , placing over the door of his school the inscription , " Let no ...
... given lines . Plato , the " poetical philosopher , " delighted in the science and culti- vated it with great success . He made mathematics the basis of his in- struction , placing over the door of his school the inscription , " Let no ...
Σελίδα 12
... given in connection with the study of each book , or after completing it , or in connection with its review . Each book should be reviewed , generally , before beginning the following book . 8. In teaching geometry , let the aim be to ...
... given in connection with the study of each book , or after completing it , or in connection with its review . Each book should be reviewed , generally , before beginning the following book . 8. In teaching geometry , let the aim be to ...
Σελίδα 18
... given above , to which the student's attention may be called as he meets them . 21. Methods of Reasoning . - There are two distinct meth- ods of geometrical reasoning , which have been distinguished as the synthetic and analytic methods ...
... given above , to which the student's attention may be called as he meets them . 21. Methods of Reasoning . - There are two distinct meth- ods of geometrical reasoning , which have been distinguished as the synthetic and analytic methods ...
Σελίδα 29
... given point only one straight line can be drawn parallel to a given line . 18. Two straight lines which have two points in com- mon coincide throughout , and form but one straight line . POSTULATES . 42. The following postulates are ...
... given point only one straight line can be drawn parallel to a given line . 18. Two straight lines which have two points in com- mon coincide throughout , and form but one straight line . POSTULATES . 42. The following postulates are ...
Άλλες εκδόσεις - Προβολή όλων
Plane Geometry: A Complete Course in the Elements of the Science Edward Brooks, Jr. Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABC and DEF ABCD AC² acute angle adjacent angles altitude angle equal angles ACD angles are equal apothem base BC² bisector centre chord circumference circumscribed circle construct a square decagon denote diagonals diameter distance divided draw equal angles equally distant equiangular equiangular polygon equilateral triangle exterior angle figure geometry given angle given circle given line given point greater Hence homologous hypotenuse inches inscribed circle inscribed regular intersect isosceles triangle Let ABC line joining mean proportional measured by one-half middle points number of sides obtuse parallel parallelogram perimeter perpendicular Proof PROPOSITION prove quadrilateral quantities radii radius ratio rectangle regular hexagon regular polygon respectively equal rhombus right angles right triangle SCHOLIUM secant segments similar square equivalent suppose tangent theorem trapezoid triangle ABC triangles are equal vertex vertical angle Whence
Δημοφιλή αποσπάσματα
Σελίδα 112 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Σελίδα 244 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 60 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Σελίδα 57 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 28 - AXIOMS. 1. 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.
Σελίδα 48 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.
Σελίδα 53 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 183 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Σελίδα 156 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Σελίδα 179 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.