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 98
... proportional . b e Given a , b and a ' , b ' corresponding sides in two similar triangles . a a ' FIG . 94 . To prove the proportion a : b = a ' : b ' . Proof . We consider first the special case , where the angles included by a , b and ...
... proportional . b e Given a , b and a ' , b ' corresponding sides in two similar triangles . a a ' FIG . 94 . To prove the proportion a : b = a ' : b ' . Proof . We consider first the special case , where the angles included by a , b and ...
Seite 100
... proportional . 238. Corollary to 234. Parallels are divided proportionally by any three copunctal transversals . 239. Corollary to 235. Two triangles are similar if they have two sides proportional and the in- cluded angles congruent ...
... proportional . 238. Corollary to 234. Parallels are divided proportionally by any three copunctal transversals . 239. Corollary to 235. Two triangles are similar if they have two sides proportional and the in- cluded angles congruent ...
Seite 101
... proportional between the parts of the hypothenuse . Each side is the mean propor- tional between the hypothenuse and its adjoining part . Proof . The r't △ ABC △ ABD , since B ~ r't D FIG . 98 . A is common . B D FIG . 99 . 245 ...
... proportional between the parts of the hypothenuse . Each side is the mean propor- tional between the hypothenuse and its adjoining part . Proof . The r't △ ABC △ ABD , since B ~ r't D FIG . 98 . A is common . B D FIG . 99 . 245 ...
Seite 102
... proportional between the parts of the diameter . 246. Theorem . The square of the hypothenuse equals the sum of the squares of the two sides . Proof . AC : AB = AB : AD , that is , ABAC AD . Same way BC2 = AC DC . Now add . .. AB2 + BC2 ...
... proportional between the parts of the diameter . 246. Theorem . The square of the hypothenuse equals the sum of the squares of the two sides . Proof . AC : AB = AB : AD , that is , ABAC AD . Same way BC2 = AC DC . Now add . .. AB2 + BC2 ...
Seite 105
... proportional to any two corresponding sides . Ex . 231. To divide a sect into parts proportional to given sects . Ex . 232. A sect can be divided into any number of equal parts . Ex . 233. To find the fourth proportional to three given ...
... proportional to any two corresponding sides . Ex . 231. To divide a sect into parts proportional to given sects . Ex . 232. A sect can be divided into any number of equal parts . Ex . 233. To find the fourth proportional to three given ...
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Häufige Begriffe und Wortgruppen
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.