The Elements of Euclid, with Many Additional Propositions and Explanatory Notes. ... Part II.1876 |
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Page 71
... vertex per- pendicular to its base . SCHOLIUM . Any side of a figure may be assumed as its base , and its altitude is the perpendicular distance from such side to the inost remote point in the figure . 4 B E C D PROPOSITION I. THEOREM ...
... vertex per- pendicular to its base . SCHOLIUM . Any side of a figure may be assumed as its base , and its altitude is the perpendicular distance from such side to the inost remote point in the figure . 4 B E C D PROPOSITION I. THEOREM ...
Page 72
... vertices of the triangles to the bases , then , because the perpen- diculars are both equal and parallel to one another ( a ) , ( a ) I. 28 . ( b ) I. 33 . the straight line which joins the vertices is parallel to that in which their ...
... vertices of the triangles to the bases , then , because the perpen- diculars are both equal and parallel to one another ( a ) , ( a ) I. 28 . ( b ) I. 33 . the straight line which joins the vertices is parallel to that in which their ...
Page 73
... vertex ( DA , EA ) ; that is , BD is to DA , as CE is to EA . [ 2 . ] — In a triangle ( ABC ) if the sides , or sides produced , be cut by a straight line ( DE ) , so that their segments between the straight line and the base ( BD , CE ) ...
... vertex ( DA , EA ) ; that is , BD is to DA , as CE is to EA . [ 2 . ] — In a triangle ( ABC ) if the sides , or sides produced , be cut by a straight line ( DE ) , so that their segments between the straight line and the base ( BD , CE ) ...
Page 74
... the varying position which the line DE may have in reference to the triangle , viz . beyond either the vertex or the base , or between them . COROLLARY . THEOREM . If several parallels ( DE , 74 ELEMENTS OF GEOMETRY .
... the varying position which the line DE may have in reference to the triangle , viz . beyond either the vertex or the base , or between them . COROLLARY . THEOREM . If several parallels ( DE , 74 ELEMENTS OF GEOMETRY .
Page 76
... vertex to the point of section bisects the exterior angle ( CAE ) of the triangle . DEMONSTRATION [ 1. ] Let the exterior angle CAE of any triangle ABC , be bisected by the straight line AD which meets the base produced in D ; then BD ...
... vertex to the point of section bisects the exterior angle ( CAE ) of the triangle . DEMONSTRATION [ 1. ] Let the exterior angle CAE of any triangle ABC , be bisected by the straight line AD which meets the base produced in D ; then BD ...
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The Elements of Euclid, with Many Additional Propositions, and Explanatory ... Euclides No preview available - 2016 |
Common terms and phrases
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
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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.