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 4
... placed that they may be omitted without breaking the chain of demonstration , and the remainder may be used as an abridged course in those schools where the time allotted to the study does not suffice for the perusal of the whole . Such ...
... placed that they may be omitted without breaking the chain of demonstration , and the remainder may be used as an abridged course in those schools where the time allotted to the study does not suffice for the perusal of the whole . Such ...
Σελίδα 13
... placed upon the other so that they shall coincide . Thus , the angles AOB and A ' O'B ' are equal , if A ' O'B ' can be superposed upon AOB so that while O'A ' coin- cides with OA , O'B ' shall also coincide with OB . The equality of ...
... placed upon the other so that they shall coincide . Thus , the angles AOB and A ' O'B ' are equal , if A ' O'B ' can be superposed upon AOB so that while O'A ' coin- cides with OA , O'B ' shall also coincide with OB . The equality of ...
Σελίδα 31
... placed so that its base BC coin- B cides with its equal EF , but so that the vertex A falls on the opposite side A H E of EF from D , as at G ; and join DG which intersects EF in H. Then , by hypothesis , EG = ED and FG BOOK I. 31.
... placed so that its base BC coin- B cides with its equal EF , but so that the vertex A falls on the opposite side A H E of EF from D , as at G ; and join DG which intersects EF in H. Then , by hypothesis , EG = ED and FG BOOK I. 31.
Σελίδα 36
... equal angles , and similarly placed , are homologous sides ; thus A and A ' are homologous angles , AB and A'B ' are homologous sides , etc. - Two polygons are mutually equilateral when the sides of the 36 GEOMETRY .
... equal angles , and similarly placed , are homologous sides ; thus A and A ' are homologous angles , AB and A'B ' are homologous sides , etc. - Two polygons are mutually equilateral when the sides of the 36 GEOMETRY .
Σελίδα 37
... placed , are homologous ; thus MN and M'N ' are homologous sides ; M and M ' are homologous angles . Two mutually equiangular polygons are not necessarily also mu- tually equilateral . Nor are two mutually equilateral polygons ...
... placed , are homologous ; thus MN and M'N ' are homologous sides ; M and M ' are homologous angles . Two mutually equiangular polygons are not necessarily also mu- tually equilateral . Nor are two mutually equilateral polygons ...
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...