Plane Geometry: A Complete Course in the Elements of the ScienceChristopher Sower Company, 1901 - 266 sider |
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Side 127
... the right angle of the triangle . SUGGESTION . - Describe a circle upon the hypotenuse as a diameter , draw the line , and compare the angles formed . LOCI OF THE CIRCLE . 1. What is the locus THEOREMS FOR DEMONSTRATION . 127.
... the right angle of the triangle . SUGGESTION . - Describe a circle upon the hypotenuse as a diameter , draw the line , and compare the angles formed . LOCI OF THE CIRCLE . 1. What is the locus THEOREMS FOR DEMONSTRATION . 127.
Side 130
... describe two arcs cutting each other in D ; and draw CD . Then CD is the perpendicular required . Proof . For the line CD has two points each equally distant from the extremities of the line AB ; it is therefore perpendicular to the ...
... describe two arcs cutting each other in D ; and draw CD . Then CD is the perpendicular required . Proof . For the line CD has two points each equally distant from the extremities of the line AB ; it is therefore perpendicular to the ...
Side 131
... describe an indefinite arc B'C ; from B ' as a centre and a radius equal to the chord AB , describe an arc cutting the indefinite arc B'C in A ' . Then the arc A'B ' will be equal to the arc AB . Proof . Draw the chord A'B ' and the ...
... describe an indefinite arc B'C ; from B ' as a centre and a radius equal to the chord AB , describe an arc cutting the indefinite arc B'C in A ' . Then the arc A'B ' will be equal to the arc AB . Proof . Draw the chord A'B ' and the ...
Side 132
... describe the arc EG , cutting the sides of the angle in E and G , and draw the chord EG . From A as a centre , with the same radius , describe the arc CB ; then , with B as a centre , and a radius equal to the chord EG , describe an arc ...
... describe the arc EG , cutting the sides of the angle in E and G , and draw the chord EG . From A as a centre , with the same radius , describe the arc CB ; then , with B as a centre , and a radius equal to the chord EG , describe an arc ...
Side 133
... describe the arc AB , and bisect this arc by the line CD , as in the previous case . Then CD will also bisect the angle ACB . Proof . For , since the arc AD equals the arc DB , as shown above , the angle ACD , measured by the arc AD ...
... describe the arc AB , and bisect this arc by the line CD , as in the previous case . Then CD will also bisect the angle ACB . Proof . For , since the arc AD equals the arc DB , as shown above , the angle ACD , measured by the arc AD ...
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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.