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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Σελίδα 29
... difference of the other two . For , if from each member of the inequality BC we subtract AB , we shall have AB + AC BC ABAC , or AC > BC — AB . - PROPOSITION XVIII . - THEOREM . 68. The sum of the three angles of any triangle is equal ...
... difference of the other two . For , if from each member of the inequality BC we subtract AB , we shall have AB + AC BC ABAC , or AC > BC — AB . - PROPOSITION XVIII . - THEOREM . 68. The sum of the three angles of any triangle is equal ...
Σελίδα 61
... difference of a and b , even when a = b , and there is really no differ- ence between a and b . - PROPOSITION XII . - THEOREM . 29. Two parallels intercept equal arcs on a circumference . We may have three cases : 1st . When the ...
... difference of a and b , even when a = b , and there is really no differ- ence between a and b . - PROPOSITION XII . - THEOREM . 29. Two parallels intercept equal arcs on a circumference . We may have three cases : 1st . When the ...
Σελίδα 64
... difference of their radii . Let O and O ' be their centres , and A one of their points of intersection . The point A is not in the line joining the centres ( 34 ) ; and consequently there is formed the triangle A00 ' , in which we have ...
... difference of their radii . Let O and O ' be their centres , and A one of their points of intersection . The point A is not in the line joining the centres ( 34 ) ; and consequently there is formed the triangle A00 ' , in which we have ...
Σελίδα 65
... difference , the circumferences intersect . 4th . When the distance of the centres is equal to the difference of the radii , the circumferences touch each other internally . 5th . When the distance of the centres is less than the ...
... difference , the circumferences intersect . 4th . When the distance of the centres is equal to the difference of the radii , the circumferences touch each other internally . 5th . When the distance of the centres is less than the ...
Σελίδα 73
... difference of the angles BAD and CAD is one - half the difference of the arcs BD and CD ; that is , the measure of the angle BAC is one - half the arc BC . 58. Corollary I. All the angles BAC , BDC , etc. , inscribed in the same segment ...
... difference of the angles BAD and CAD is one - half the difference of the arcs BD and CD ; that is , the measure of the angle BAC is one - half the arc BC . 58. Corollary I. All the angles BAC , BDC , etc. , inscribed in the same segment ...
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.