A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern GeometryJ.B. Lippincott, 1872 - 368 σελίδες |
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Σελίδα 257
... polar triangle of the first . Thus , if A , B and C are the poles of the arcs of great circles , B'C ' , A'C ' , and A'B ' , respec- tively , A'B'C ' is the polar triangle of ABC . B ' B Since all great circles , when completed ...
... polar triangle of the first . Thus , if A , B and C are the poles of the arcs of great circles , B'C ' , A'C ' , and A'B ' , respec- tively , A'B'C ' is the polar triangle of ABC . B ' B Since all great circles , when completed ...
Σελίδα 260
... polar triangle of M , and N ' the polar triangle of N. Since M and N are mutually equiangular , their polar triangles M ' and N ' are mutually equi- lateral ( 69 ) ; therefore , by the preceding proposition , the triangles M ' and N ...
... polar triangle of M , and N ' the polar triangle of N. Since M and N are mutually equiangular , their polar triangles M ' and N ' are mutually equi- lateral ( 69 ) ; therefore , by the preceding proposition , the triangles M ' and N ...
Σελίδα 261
... polar triangle of ABC . Then , the sides A'B ' and A'C ' are equal ( 69 ) , and therefore the angles B ' and C ' are equal ( 78 ) . But since the angles B ' and C ' are equal in the triangle A'B'C ' , the sides AB and AC are equal in ...
... polar triangle of ABC . Then , the sides A'B ' and A'C ' are equal ( 69 ) , and therefore the angles B ' and C ' are equal ( 78 ) . But since the angles B ' and C ' are equal in the triangle A'B'C ' , the sides AB and AC are equal in ...
Σελίδα 263
... polar triangle by a ' , b ' , c ' , we have ( 70 ) , A180 ° -a ' , B = 180 ° - b ' , C = 180 ° - c ' , the sum of which is A + B + C540 ° ( a ' + b ' + c ' ) . A B ' A ' But a'b ' + c ' < 360 ° ( 86 ) ; therefore , A + B + C > 180 ...
... polar triangle by a ' , b ' , c ' , we have ( 70 ) , A180 ° -a ' , B = 180 ° - b ' , C = 180 ° - c ' , the sum of which is A + B + C540 ° ( a ' + b ' + c ' ) . A B ' A ' But a'b ' + c ' < 360 ° ( 86 ) ; therefore , A + B + C > 180 ...
Σελίδα 269
... polar dis- tances AC and BC , describe circumferences on the surface ; these circumferences touch at C and lie wholly without each other . For , let M be any point in the circumference whose pole is A , and draw the arcs of great ...
... polar dis- tances AC and BC , describe circumferences on the surface ; these circumferences touch at C and lie wholly without each other . For , let M be any point in the circumference whose pole is A , and draw the arcs of great ...
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 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
Δημοφιλή αποσπάσματα
Σελίδα 128 - The area of a rectangle is equal to the product of its base and altitude.
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 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Σελίδα 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.
Σελίδα 29 - The sum of the three angles of any triangle is equal to two right angles.
Σελίδα 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.
Σελίδα 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...
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 197 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.
Σελίδα 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R...