The text of Euclid's geometry, book 1, uniformly and systematically arranged by J.D. Paul1884 |
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... definitions , postulates , axioms and former propositions , necessary for the construction and demonstration are stated . The blank spaces left may be found useful for notes . The only abbreviations used are : - A , for vi PREFACE .
... definitions , postulates , axioms and former propositions , necessary for the construction and demonstration are stated . The blank spaces left may be found useful for notes . The only abbreviations used are : - A , for vi PREFACE .
Page 1
... space magnitudes generally . It is the most important of all mathematical sciences ; Astronomy , Navigation , Surveying , Perspective , Mechanics etc. , all depend upon it , and before the student can proceed to the study of such ...
... space magnitudes generally . It is the most important of all mathematical sciences ; Astronomy , Navigation , Surveying , Perspective , Mechanics etc. , all depend upon it , and before the student can proceed to the study of such ...
Page 2
... space around us . Length , breadth , and thickness are called dimensions of space . Space can be of either one , two , or three dimensions . The distance of one star from another is a space of one dimension , viz . length . A shadow on ...
... space around us . Length , breadth , and thickness are called dimensions of space . Space can be of either one , two , or three dimensions . The distance of one star from another is a space of one dimension , viz . length . A shadow on ...
Page 3
... space ; a superficies is a magnitude and space ; but a point is neither a magnitude nor space . An angle is a magnitude but not space ; it is the magnitude formed by the turning of one line about a point in another , the lengths of the ...
... space ; a superficies is a magnitude and space ; but a point is neither a magnitude nor space . An angle is a magnitude but not space ; it is the magnitude formed by the turning of one line about a point in another , the lengths of the ...
Page 4
... space , the limits or bounds of which are either lines or superficies . " Euclid's definition of parallel straight lines is a negative definition . It would be impossible to determine from it whether lines were parallel ; for , however ...
... space , the limits or bounds of which are either lines or superficies . " Euclid's definition of parallel straight lines is a negative definition . It would be impossible to determine from it whether lines were parallel ; for , however ...
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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