A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |
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Page 12
... opposite B sides of O , may be regarded as two different lines having opposite directions reckoned from the common origin 0 . Hence , also , every straight line AB has two opposite directions , namely , from A toward B ( A being ...
... opposite B sides of O , may be regarded as two different lines having opposite directions reckoned from the common origin 0 . Hence , also , every straight line AB has two opposite directions , namely , from A toward B ( A being ...
Page 17
... sides are in the same straight line . Let the sum of the adjacent angles AOD , BOD , be equal to two right angles ... opposite ( or vertical ) angles are equal . Let AB and CD intersect in 0 ; then will the opposite , or vertical ...
... sides are in the same straight line . Let the sum of the adjacent angles AOD , BOD , be equal to two right angles ... opposite ( or vertical ) angles are equal . Let AB and CD intersect in 0 ; then will the opposite , or vertical ...
Page 21
... opposite sides of the perpendicular , as PE and PD ' , and if CE > CD ' , take CD CD ' , and join PD . Then , as above PE > PD ; and , by Proposition VII . , PD PD ' ; hence PE PD ' . = 36. Corollary I. ( Converse of Proposition VII ...
... opposite sides of the perpendicular , as PE and PD ' , and if CE > CD ' , take CD CD ' , and join PD . Then , as above PE > PD ; and , by Proposition VII . , PD PD ' ; hence PE PD ' . = 36. Corollary I. ( Converse of Proposition VII ...
Page 24
... opposite sides of F 4 1 D 7 6 8 5 3 2 B E the secant line and not adjacent - as 1 , 3 - or 2 , 4 - are called alter- nate - exterior angles . Two interior angles on opposite sides of the secant line and not adjacent - as 5 , 7 - or 6 ...
... opposite sides of F 4 1 D 7 6 8 5 3 2 B E the secant line and not adjacent - as 1 , 3 - or 2 , 4 - are called alter- nate - exterior angles . Two interior angles on opposite sides of the secant line and not adjacent - as 5 , 7 - or 6 ...
Page 26
... side of the secant line is equal to two right angles , the two lines are parallel . 57. Corollary III . From ( 52 ) ... opposite sides CI of AB , at the given distance from it . PROPOSITION XVI . - THEOREM . 60. If two angles 26 GEOMETRY .
... side of the secant line is equal to two right angles , the two lines are parallel . 57. Corollary III . From ( 52 ) ... opposite sides CI of AB , at the given distance from it . PROPOSITION XVI . - THEOREM . 60. If two angles 26 GEOMETRY .
Other editions - View all
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2015 |
Common terms and phrases
ABCD AC² adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone 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 hypotenuse indefinitely inscribed angle isosceles Let ABC measure medial lines 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
Popular passages
Page 128 - The area of a rectangle is equal to the product of its base and altitude.
Page 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...
Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 79 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Page 29 - The sum of the three angles of any triangle is equal to two right angles.
Page 175 - If a straight line is perpendicular to each of two straight lines at' their point of intersection, it is perpendicular to the plane of those lines.
Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 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.
Page 197 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.
Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R...