Euclidian Geometry |
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Page v
... Theorems , both classified according to the nature of the subject , and demonstrations replaced by others less ... theorem is assumed as self - evident which certainly requires proof as much as those which are made to depend upon ...
... Theorems , both classified according to the nature of the subject , and demonstrations replaced by others less ... theorem is assumed as self - evident which certainly requires proof as much as those which are made to depend upon ...
Page vii
... Theorems , should nevertheless occupy the attention of the beginner as soon as possible , and also that the necessity of his having to wade through a long book of Theorems only should be avoided . This has been effected by placing the ...
... Theorems , should nevertheless occupy the attention of the beginner as soon as possible , and also that the necessity of his having to wade through a long book of Theorems only should be avoided . This has been effected by placing the ...
Page xiv
... Theorems on Proportion made use of to be stated . Any proofs allowed , the Axiom or Lemma on which they depend being stated . Any proofs allowed , the With regard to Euc . VI . Definition or test of Pro- I. 33 . portion being stated ...
... Theorems on Proportion made use of to be stated . Any proofs allowed , the Axiom or Lemma on which they depend being stated . Any proofs allowed , the With regard to Euc . VI . Definition or test of Pro- I. 33 . portion being stated ...
Page 36
... ( I. 13 ) .. PQ , RS do not meet when produced towards Q , S. Similarly it may be proved that they will not meet if produced towards P , R. .. they are parallel . Hence are easily deduced the following Theorems : If a 36 PARALLELS .
... ( I. 13 ) .. PQ , RS do not meet when produced towards Q , S. Similarly it may be proved that they will not meet if produced towards P , R. .. they are parallel . Hence are easily deduced the following Theorems : If a 36 PARALLELS .
Page 37
Francis Cuthbertson. Hence are easily deduced the following Theorems : If a straight line , falling upon two other straight lines . makes the exterior angle equal to the interior and opposite upon the same side of the line , the two ...
Francis Cuthbertson. Hence are easily deduced the following Theorems : If a straight line , falling upon two other straight lines . makes the exterior angle equal to the interior and opposite upon the same side of the line , the two ...
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Common terms and phrases
Algebra Arithmetic base BEGINNERS Cambridge centre chord Christ's College circumference cloth Conic Sections Crown 8vo Describe a circle diagonals diameter divided ELEMENTARY TREATISE English equiangular equilateral Euclid Examples Extra fcap GEOMETRY given angle given circle given point given straight line Grammar greater H Let Hence inscribed intersecting isosceles triangle John's College Latin Let ABC line bisecting locus magnitudes Mathematical meet Owens College parallel parallelogram perimeter perpendicular plane PROBLEM produced Professor proportional PROPOSITION radius ratio rect rectangle rectangle contained rectilineal figure regular polygon render respectively revised rhombus right angles Schools Second Edition segment Similarly squares on AC straight line joining student tangent THEOREM TRIGONOMETRY twice rectangle twice the squares Uppingham School vertex
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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 15 - ... and the principles on which the observations made with these instruments are treated for deduction of the distances and weights of the bo.iits of the Solar System, and of a few stars, omitting all minutiit of Elementary Class- Books — continued. formulcE, and all troublesome details of calculation.