Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's FoundationsJ. Wiley & Sons, 1904 - 285 Seiten |
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Seite 3
... Theorem . Two straights have one or no point in common . Proof . By 6 they cannot have two . 8. Theorem . Two planes have no point or a straight in common . Proof . If they have one point in common , then ( by I 6 ) they have a second ...
... Theorem . Two straights have one or no point in common . Proof . By 6 they cannot have two . 8. Theorem . Two planes have no point or a straight in common . Proof . If they have one point in common , then ( by I 6 ) they have a second ...
Seite 4
... Theorem . A plane and a straight not lying in it have no point or one point in common . Proof . If they had two points in common the straight would be ( by I 5 ) situated completely in the plane . 11. Theorem . Through a straight and a ...
... Theorem . A plane and a straight not lying in it have no point or one point in common . Proof . If they had two points in common the straight would be ( by I 5 ) situated completely in the plane . 11. Theorem . Through a straight and a ...
Seite 6
... Theorem . Between any two points of a straight there are always indefinitely many points . [ Here taken for granted , and its proof removed to Appendix I. ] 17. Theorem . If any finite number of points of 1 a straight are given , then ...
... Theorem . Between any two points of a straight there are always indefinitely many points . [ Here taken for granted , and its proof removed to Appendix I. ] 17. Theorem . If any finite number of points of 1 a straight are given , then ...
Seite 7
... theorem is here taken for granted , and its proof removed to Appendix I. ] 21. Theorem . If A , B , C be not costraight , any straight in the plane ABC which has a point within the sect AB and a point within AC cannot have a point ...
... theorem is here taken for granted , and its proof removed to Appendix I. ] 21. Theorem . If A , B , C be not costraight , any straight in the plane ABC which has a point within the sect AB and a point within AC cannot have a point ...
Seite 19
... theorem for triangles . ) Triangles are congruent if they have two sides and the included angle congruent . FIG . 13 . In the triangles ABC and A'B'C ' take AB = A'B ' , AC = A'C ' , A = × A ' . - To prove ABC = ^ A'B'C ' . Proof ...
... theorem for triangles . ) Triangles are congruent if they have two sides and the included angle congruent . FIG . 13 . In the triangles ABC and A'B'C ' take AB = A'B ' , AC = A'C ' , A = × A ' . - To prove ABC = ^ A'B'C ' . Proof ...
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adjacent angles altitude angle h angles opposite assumptions axis base bisection-point bisector bisects called chord circle circumcenter congruent congruent angles Construction coplanar copunctal Corollary costraight Definition determine diagonals diameter dicular draw edges end-points Engineering equilateral equivalent by completion face-angles Find the locus frustum Geometry given angle given plane given point given sect given straight greater gruent hypothenuse hypothesis inscribed inscribed angle intersection Inverse isosceles triangle joining Manual median meet meters minor arc morocco opposite sides orthocenter pair parallel parallelogram part-tetrahedra perigon perpen perpendicular point in common polar pole polygon polyhedron prismatoid Problem Proof proportional prove pyramid quad quadrant quadrilateral radius right angles sphere spherical angle spherical polygon spherical triangle square st's straightest summits supplemental symmetrical tangent Text-book Theorem third side transversal partitions Treatise triangle ABC trihedral unit sect vertex vertices
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Seite 293 - Fuertes's Water and Public Health i2mo, i 50 Water-filtration Works. i2mo, 2 50 Ganguillet and Kutter's General Formula for the Uniform Flow of Water in Rivers and Other Channels.
Seite 294 - Trautwine's Method of Calculating the Cubic Contents of Excavations and Embankments by the Aid of Diagrams 8vo, 2 oo The Field Practice of {Laying Out Circular Curves for Railroads.
Seite 299 - Part II. Design, Construction, and Operation 8vo, 6 oo Handbook of Engine and Boiler Trials, and the Use of the Indicator and the Prony Brake 8vo, 5 oo Stationary Steam-engines 8vo...
Seite 300 - Power of Transmission. (Herrmann — Klein.) 8vo, 5 oo Machinery of Transmission and Governors. (Herrmann — Klein.). 8vo, 5 oo Wood's Elements of Analytical Mechanics 8vo, 3 oo Principles of Elementary Mechanics i2mo, i 25 Turbines • 8vo, 2 50 The World's Columbian Exposition of 1893 4to, i oo METALLURGY. Egleston's Metallurgy of Silver, Gold, and Mercury: Vol.
Seite 292 - Wilson's Topographic Surveying 8vo, 3 50 BRIDGES AND ROOFS. Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 2 oo * Thames River Bridge 4to, paper...
Seite 239 - If two triangles have two sides of the one equal to two sides of the...
Seite 293 - I2mo, 60 Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 3d Edition, Rewritten 8vo, 4 oo Examination of Water.
Seite 300 - Machinery 8vo, i 50 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo Kerr's Power and Power Transmission 8vo...
Seite 289 - Bernadou's Smokeless Powder. — Nitro-cellulose, and Theory of the Cellulose Molecule 12mo, 2 50 * Biltz's Introduction to Inorganic Chemistry. (Hall and Phelan.). . . 12mo, 1 25 Laboratory Methods of Inorganic Chemistry. (Hall and Blanchard.) 8vo, 3 00 * Blanchard's Synthetic Inorganic Chemistry 12mo, 1 00 * Browning's Introduction to the Rarer Elements 8vo, 1 50 * Claassen's Beet-sugar Manufacture.