The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 1
... passes through all the angular points of the figure about which it is circumscribed . 7. A straight line is said to be placed in a circle , when its extremities are in the circumference of the circle . B SCHOLIUM . A regular polygon is ...
... passes through all the angular points of the figure about which it is circumscribed . 7. A straight line is said to be placed in a circle , when its extremities are in the circumference of the circle . B SCHOLIUM . A regular polygon is ...
Page 5
... passes through the points E and G , and because the angles at F , E , and G are right angles , the lines BC , AB , and AC are tan- gents to the circle ( i ) ; therefore the circle FEG is inscribed in the given triangle ( k ) . SCHOLIUM ...
... passes through the points E and G , and because the angles at F , E , and G are right angles , the lines BC , AB , and AC are tan- gents to the circle ( i ) ; therefore the circle FEG is inscribed in the given triangle ( k ) . SCHOLIUM ...
Page 6
... passing through them in the manner demonstrated in the theorem attached to III . 1 . A D B A E B C E F B D E F SCHOLIA . 1. This proposition has been anticipated by the theorem above - mentioned . 2. If the center F fall within the ...
... passing through them in the manner demonstrated in the theorem attached to III . 1 . A D B A E B C E F B D E F SCHOLIA . 1. This proposition has been anticipated by the theorem above - mentioned . 2. If the center F fall within the ...
Page 9
... the center E with the radius AE passes through the angular points , A , B , C , and D , and is circumscribed about the given square PROPOSITION X. PROBLEM . To construct an isosceles triangle , B 3 ELEMENTS OF GEOMETRY . 9.
... the center E with the radius AE passes through the angular points , A , B , C , and D , and is circumscribed about the given square PROPOSITION X. PROBLEM . To construct an isosceles triangle , B 3 ELEMENTS OF GEOMETRY . 9.
Page 111
... passes through its center , and is terminated both ways by the superficies of the sphere . 16. A CONE is a solid figure described by the revolution of a right - angled triangle about one of the sides containing the right angle , which ...
... passes through its center , and is terminated both ways by the superficies of the sphere . 16. A CONE is a solid figure described by the revolution of a right - angled triangle about one of the sides containing the right angle , which ...
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The Elements of Euclid, with Many Additional Propositions, and Explanatory ... Euclides No preview available - 2016 |
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altitude angle ABC angle BAC base ABC base DEF base EH bisected circle ABCD circle EFGH circumference common section cone Construction contained COROLLARY cylinder DEMONSTRATION duplicate ratio equal and similar equal angles equi equiangular equimultiples Euclid ex æquali fore four magnitudes fourth given circle given straight line greater ratio homologous homologous sides Hypoth inscribed join less LUDGATE HILL multiple opposite planes paral parallel parallelogram perpendicular polygon polyhedron prism PROPOSITION pyramid ABCG pyramid DEFH RALPH TATE reciprocally proportional rectangle rectilineal figure remaining angle right angles SCHOLIUM segments solid angle solid CD solid parallelopipeds sphere square on BD THEOREM THEOREM.-If third three plane angles three straight lines tiple triangle ABC triplicate ratio vertex vertex the point wherefore Woodcuts
Popular passages
Page 10 - A KEY AND COMPANION to the above Book, forming an extensive repository of Solved Examples and Problems in Illustration of the various Expedients necessary in Algebraical Operations.
Page 111 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 14 - ... Practical Form. With a Course of Exercises. By ALFRED ELWES. is. 6d. 35. Spanish-English and English-Spanish Dictionary. Including a large number of Technical Terms used in Mining, Engineering, &c., with the proper Accents and the Gender of every Noun. By ALFRED ELWES.
Page 5 - SHIPBUILDING, NAVIGATION, MARINE ENGINEERING, ETC. 51. NAVAL ARCHITECTURE, the Rudiments of; or an Exposition of the Elementary Principles of the Science, and their Practical Application to Naval Construction. Compiled for the Use of Beginners. By JAMES PEAKE, School of Naval Architecture, HM Dockyard, Portsmouth.
Page 85 - ... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another.
Page 7 - Comprising Observations on the Materials from, and Processes by which, they are manufactured ; their Special Uses, Applications, Qualities, and Efficiency.
Page 18 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding...
Page 7 - By DIONYSIUS LARDNER, DCL, formerly Professor of Natural Philosophy and Astronomy in University College, London.