## Euclidian Geometry |

### From inside the book

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**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

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**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

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**Theorems**on Proportion made use of to be stated . Any proofs allowed , the Axiom or Lemma on which they depend being stated . With regard to Euc . VI . Any proofs allowed , the Definition or test of Pro- portion being stated . 1. 33 ... 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

... ( 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

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 ...### Other editions - View all

### Common terms and phrases

base bisect Cambridge centre chapter chord circle circumference classes cloth College common complete construction contained Crown 8vo DEFINITION describe diameter difference divided double draw drawn Edition elementary English equal equiangular Examination Examples extremities fall fcap figure former four GEOMETRY given point given straight line Grammar greater Hence Illustrations impossible inscribed introduction Join language Latin less magnitudes Master Mathematical meet method Notes opposite parallel parallelogram pass perimeter perpendicular plane polygon possible present principles PROBLEM produced Professor proportional PROPOSITION prove ratio reading rect rectangle render respectively revised right angles Schools Second Edition segment selected sides similar Similarly square student taken tangent THEOREM third touch TREATISE triangle twice University volume whole

### Popular passages

Page 1 - ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.

Page 10 - New Edition. Crown 8vo. $s. KEY TO PLANE TRIGONOMETRY. Crown 8vo. los. 6d. A TREATISE ON SPHERICAL TRIGONOMETRY. New Edition, enlarged. Crown 8vo. 4-?. 6d. PLANE CO-ORDINATE GEOMETRY, as applied to the Straight Line and the Conic Sections. With numerous Examples.

Page 42 - Friends," with briefer Notes. i8mo. 3*. 6d. GREEK TESTAMENT. Edited, with Introduction and Appendices, by CANON WESTCOTT and Dr. FJA HORT. Two Vols. Crown 8vo. [/« the press. HARDWICK — Works by Archdeacon HARDWICK. A HISTORY OF THE CHRISTIAN CHURCH. Middle Age. From Gregory the Great to the Excommunication of Luther. Edited by WILLIAM STUBBS, MA, Regius Professor of Modern History in the University of Oxford. With Four Maps constructed for this work by A. KEITH JOHNSTON.

Page 31 - HISTORICAL OUTLINES OF ENGLISH ACCIDENCE, comprising Chapters on the History and Development of the Language, and on Word-formation.

Page 15 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.

Page 47 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.

Page 45 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.

Page 12 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.

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.