The text of Euclid's geometry, book 1, uniformly and systematically arranged by J.D. Paul1884 |
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Side 10
... unequal . If the same magnitude be taken from unequals the remainders are unequal . Magnitudes which are double of equal magnitudes are equal to one another . Magnitudes which are halves of equal magnitudes are equal to one another ...
... unequal . If the same magnitude be taken from unequals the remainders are unequal . Magnitudes which are double of equal magnitudes are equal to one another . Magnitudes which are halves of equal magnitudes are equal to one another ...
Side 11
... unequal magnitudes one must be greater than the other . ( n ) One magnitude cannot be both equal to and greater than another . ( 0 ) If one magnitude is not equal to nor less than a second magni- tude , the first is greater than the ...
... unequal magnitudes one must be greater than the other . ( n ) One magnitude cannot be both equal to and greater than another . ( 0 ) If one magnitude is not equal to nor less than a second magni- tude , the first is greater than the ...
Side 15
... An equilateral triangle ABC , and a scalene triangle ADE , have the same vertical angle at A , and the point D is in AB produced ; it is required to show that BD is not equal to CE . B W AD is unequal to AE , and AB is equal GEOMETRY . 15.
... An equilateral triangle ABC , and a scalene triangle ADE , have the same vertical angle at A , and the point D is in AB produced ; it is required to show that BD is not equal to CE . B W AD is unequal to AE , and AB is equal GEOMETRY . 15.
Side 16
... unequal ; the absurdity of this can be easily shown thus : — B E Let AB and DE be two equal straight lines , and let AB be divided into two unequal parts at the point C , so that AC is greater than CB ; suppose from DE a part DF be cut ...
... unequal ; the absurdity of this can be easily shown thus : — B E Let AB and DE be two equal straight lines , and let AB be divided into two unequal parts at the point C , so that AC is greater than CB ; suppose from DE a part DF be cut ...
Side 32
... unequal . This proposition is not required by Euclid in his first book , and might have been proved directly by the twenty - sixth proposition . I. 7. This proposition is demonstrated only in order to prove the eighth proposition . The ...
... unequal . This proposition is not required by Euclid in his first book , and might have been proved directly by the twenty - sixth proposition . I. 7. This proposition is demonstrated only in order to prove the eighth proposition . The ...
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2nd Edition 4th Edition AB is equal ABC and DEF ABC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle contained angle DEF angle EDF angle equal angle GHD angles are equal angles CBA Axiom 9 base BC BDC is greater bisector bisects centre circle coincide Constr Crown 8vo describe diagonal equal sides equal to BD equal to EF equilateral triangle Euclid exterior angle F. A. Paley Fcap finite straight line Geometry given point given straight line isosceles triangle Join Latin magnitude are equal opposite sides parallel to BC parallelogram parallelogram ABCD plane figure Post 8vo Postulate produced Q. E. D. PROPOSITION quadrilateral rectilineal angle REQUIRED TO PROVE rhombus right angles sides equal square on AC straight line drawn THEOREM triangle ABC triangle DEF triangles are equal vertex Нур
Populære avsnitt
Side 95 - If two triangles have two sides of the one equal to two sides of the...
Side 65 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to each other in a plane, which meet together, but are not in the same direction.
Side 13 - FBS 8vo. 10s. 6d. Language, its Origin and Development. By TH Key, MA, FRS 8vo. 14s. Synonyms and Antonyms of the English Language. By Archdeacon Smith. 2nd Edition. Post 8vo. 5s. Synonyms Discriminated. By Archdeacon Smith. Demy 8vo. 16s. Bible English. By TL 0. Davies. 5s. The Queen's English. A Manual of Idiom and Usage. By the late Dean Alford 6th Edition. Fcap. 8vo. 5s.
Side 10 - An Elementary Treatise on Mensuration. By BT Moore, MA 5s. ANALYTICAL GEOMETRY AND DIFFERENTIAL CALCULUS. An Introduction to Analytical Plane Geometry. By WP Turnbull, MA 8vo. 12s. Problems on the Principles of Plane Co-ordinate Geometry. By W. Walton, MA 8vo. 16s. Trilinear Co-ordinates, and Modern Analytical Geometry of Two Dimensions.
Side 73 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 72 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 12 - Lives of the Queens of England. By A. Strickland. Library Edition, 8 vols. 7s. 6d. each. Cheaper Edition, 6 vols. 5s. each. Abridged Edition, 1 vol. 6s. 6d.
Side 8 - Greek Verbs. A Catalogue of Verbs, Irregular and Defective; their leading formations, tenses, and inflexions, with Paradigms for conjugation, Rules for formation of tenses, &c.
Side 12 - Long. 5 vols. 8vo. 14s. each. A History of England during the Early and Middle Ages. By CH Pearson, MA 2nd Edition revised and enlarged.