Plane Geometry: A Complete Course in the Elements of the ScienceChristopher Sower Company, 1901 - 266 σελίδες |
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Σελίδα 25
... drawn . 20. Different lines drawn from the same point are said to have different directions ; as AB and AE . E B 21. If any line , as AB , is produced through A to C , the parts AB and AC , on opposite sides of A , may be regarded as ...
... drawn . 20. Different lines drawn from the same point are said to have different directions ; as AB and AE . E B 21. If any line , as AB , is produced through A to C , the parts AB and AC , on opposite sides of A , may be regarded as ...
Σελίδα 29
... drawn connecting two given points . 15. Straight lines , lying in the same plane , which cannot meet one another ... drawn parallel to a given line . 18. Two straight lines which have two points in com- mon coincide throughout , and form ...
... drawn connecting two given points . 15. Straight lines , lying in the same plane , which cannot meet one another ... drawn parallel to a given line . 18. Two straight lines which have two points in com- mon coincide throughout , and form ...
Σελίδα 30
... drawn equal to a given line . 4. From the greater of two lines a part may be cut off equal to the less . 5. Through a given point a straight line may be drawn parallel to a given straight line . NOTE . - Geometers sometimes , for ...
... drawn equal to a given line . 4. From the greater of two lines a part may be cut off equal to the less . 5. Through a given point a straight line may be drawn parallel to a given straight line . NOTE . - Geometers sometimes , for ...
Σελίδα 37
... drawn to that line . Given . - Let the line CD be perpendicular to the line AB at the point C. To Prove . Then we are to prove that at the point C no other perpendicu- lar can be drawn to AB . Proof . If it were possible , suppose Д D B ...
... drawn to that line . Given . - Let the line CD be perpendicular to the line AB at the point C. To Prove . Then we are to prove that at the point C no other perpendicu- lar can be drawn to AB . Proof . If it were possible , suppose Д D B ...
Σελίδα 38
... drawn to that line . Given . Let Pbe the given point , and PE a perpendicular to AB . To Prove . Then we are to prove that no other perpendicular to AB can be drawn from the point P. Proof . Suppose , if possible , some other line , as ...
... drawn to that line . Given . Let Pbe the given point , and PE a perpendicular to AB . To Prove . Then we are to prove that no other perpendicular to AB can be drawn from the point P. Proof . Suppose , if possible , some other line , as ...
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.