The text of Euclid's geometry, book 1, uniformly and systematically arranged by J.D. Paul1884 |
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Page
... theorems , some examples of the application of this method are given . With a view to guarding the student against some of the principal errors which beginners are liable to make when attempting to demonstrate theorems , examples of ...
... theorems , some examples of the application of this method are given . With a view to guarding the student against some of the principal errors which beginners are liable to make when attempting to demonstrate theorems , examples of ...
Page
... theorems without using diagrams . With reference to the progressive nature of the exercises , the author has taken the opinions of a great many young beginners as to their relative difficulty , and arranged them accordingly . The first ...
... theorems without using diagrams . With reference to the progressive nature of the exercises , the author has taken the opinions of a great many young beginners as to their relative difficulty , and arranged them accordingly . The first ...
Page 8
... theorem , and in the latter a problem . The postulates are problems admitted to be solved , and the axioms are theorems admitted to be true without proof . The enunciation states the nature of the proposal , first in general terms , and ...
... theorem , and in the latter a problem . The postulates are problems admitted to be solved , and the axioms are theorems admitted to be true without proof . The enunciation states the nature of the proposal , first in general terms , and ...
Page 12
... theorem is false the hypothesis is false , or , in other words , no false statement can be a necessary consequence of a true statement . Of the above statements , some are axioms , some definitions , and some postulates . They are not ...
... theorem is false the hypothesis is false , or , in other words , no false statement can be a necessary consequence of a true statement . Of the above statements , some are axioms , some definitions , and some postulates . They are not ...
Page 13
... theorems which could be demonstrated , and in some cases could be included in fewer and more general principles . They are simply facts which the student must be prepared to accept , and are mentioned here in order that every statement ...
... theorems which could be demonstrated , and in some cases could be included in fewer and more general principles . They are simply facts which the student must be prepared to accept , and are mentioned here in order that every statement ...
Common terms and phrases
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
Popular passages
Page 95 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
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Page 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...
Page 72 - LET it be granted that a straight line may be drawn from any one point to any other point.
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