A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern GeomentryJ.B. Lippincott & Company, 1871 - 368 σελίδες |
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Αποτελέσματα 1 - 5 από τα 46.
Σελίδα 12
... coincide in two points , they coincide throughout their whole extent , and form but one line . Hence two points determine a straight line ; and a straight line may be designated by any two of its points . 4. Different straight lines ...
... coincide in two points , they coincide throughout their whole extent , and form but one line . Hence two points determine a straight line ; and a straight line may be designated by any two of its points . 4. Different straight lines ...
Σελίδα 13
... coincide with OB . The equality of the two angles is not affected by producing the sides ; for the coincident sides con- tinue to coincide when produced indefinitely ( 3 ) . * Thus the magnitude of an angle is independent of the length ...
... coincide with OB . The equality of the two angles is not affected by producing the sides ; for the coincident sides con- tinue to coincide when produced indefinitely ( 3 ) . * Thus the magnitude of an angle is independent of the length ...
Σελίδα 15
... coincide and the angles will be equal ( 6 ) . PROPOSITION II . - THEOREM . 11. The two adjacent angles which one straight line makes with another are together equal to two right angles . If the two angles are equal , they are right ...
... coincide and the angles will be equal ( 6 ) . PROPOSITION II . - THEOREM . 11. The two adjacent angles which one straight line makes with another are together equal to two right angles . If the two angles are equal , they are right ...
Σελίδα 18
... coincides with P ' . Since the line AB is fixed during the revolution , the point Cis fixed ; therefore PC will coincide with P'C , and the angle PCD with the angle P'CD . These angles are therefore equal ( 6 ) , and BC is perpendicular ...
... coincides with P ' . Since the line AB is fixed during the revolution , the point Cis fixed ; therefore PC will coincide with P'C , and the angle PCD with the angle P'CD . These angles are therefore equal ( 6 ) , and BC is perpendicular ...
Σελίδα 19
... coincides with P ' , PD also coincides with P'D ; and hence PD P'D . But the straight line PP ' , being the shortest distance = P PI D -B between the points P and P ' , is less than the broken line PDP ' . Therefore PC , the half of the ...
... coincides with P ' , PD also coincides with P'D ; and hence PD P'D . But the straight line PP ' , being the shortest distance = P PI D -B between the points P and P ' , is less than the broken line PDP ' . Therefore PC , the half of the ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone construct Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw edges equally distant equilateral equivalent exterior angle faces figure find the locus frustum given circles given plane given point given straight line hence homologous indefinitely inscribed inscribed angle isosceles Let ABC measure middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 115 - X PB'; that is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment.
Σελίδα 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 127 - The areas of two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 129 - The area of a parallelogram is equal to the product of its base and altitude. Let...
Σελίδα 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Σελίδα 219 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 261 - Any side of a spherical triangle is less than the sum of the other two.
Σελίδα 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 132 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.