Plane Geometry: A Complete Course in the Elements of the ScienceChristopher Sower Company, 1901 - 266 sider |
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Side 9
... proposition of the square on the hypotenuse . It was said that in honor of the last discovery he sacrificed one hundred oxen . Plutarch , however , says but one ox ; and Cicero doubts even that , as it was in opposition to his doctrines ...
... proposition of the square on the hypotenuse . It was said that in honor of the last discovery he sacrificed one hundred oxen . Plutarch , however , says but one ox ; and Cicero doubts even that , as it was in opposition to his doctrines ...
Side 17
... proposition is not necessarily true . Thus , while " All birds are bipeds " is true , its converse , " All bipeds are birds , " is not true . 14. The relation of these three forms of the proposition is indicated in the following ...
... proposition is not necessarily true . Thus , while " All birds are bipeds " is true , its converse , " All bipeds are birds , " is not true . 14. The relation of these three forms of the proposition is indicated in the following ...
Side 19
... proposition to be proved is not true , and then showing that such a sup- position leads to a contradiction of some known truth . This proves a theorem to be true by simply showing that it cannot be false . 28. The method is frequently ...
... proposition to be proved is not true , and then showing that such a sup- position leads to a contradiction of some known truth . This proves a theorem to be true by simply showing that it cannot be false . 28. The method is frequently ...
Side 20
... proposition we employ the proposition itself . CHAPTER III . GEOMETRICAL LANGUAGE . 1. LANGUAGE is the means of expressing our ideas and thoughts . 2. We think by means of language , and hence language may be considered as an instrument ...
... proposition we employ the proposition itself . CHAPTER III . GEOMETRICAL LANGUAGE . 1. LANGUAGE is the means of expressing our ideas and thoughts . 2. We think by means of language , and hence language may be considered as an instrument ...
Side 30
... PROPOSITION is a general term applied to the- orems and problems . 49. A COROLLARY is a truth easily deduced from one or more propositions . 50. A SCHOLIUM is a remark upon one or more 30 PLANE GEOMETRY . - BOOK I. Definitions 145.
... PROPOSITION is a general term applied to the- orems and problems . 49. A COROLLARY is a truth easily deduced from one or more propositions . 50. A SCHOLIUM is a remark upon one or more 30 PLANE GEOMETRY . - BOOK I. Definitions 145.
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Plane Geometry: A Complete Course in the Elements of the Science Edward Brooks Uten tilgangsbegrensning - 1901 |
Plane Geometry: A Complete Course in the Elements of the Science Edward Brooks, Jr. Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 112 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Side 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.
Side 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.
Side 57 - In an isosceles triangle the angles opposite the equal sides are equal.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 179 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.