## Euclidian Geometry |

### From inside the book

Results 1-5 of 22

Page 161

If four magnitudes are

If four magnitudes are

**proportional**then any others which have the same ratio as the first and second are**proportional**to any others which have the same ratio as the third and fourth . For the test expressed by the definition is ... Page 162

PROPOSITION V. If four straight lines are

PROPOSITION V. If four straight lines are

**proportional**the rectangle con- tained by the extremes is equal to that contained by the means . rect rect ¡ rect ( a , c ) rect ( a , c ) ( a , d ) ( be ) a d Let the four straight lines a ... Page 163

Also when = a : bas bd , the straight lines a , b , d are then said to be

Also when = a : bas bd , the straight lines a , b , d are then said to be

**proportional**. Hence , if three straight lines are**proportional**the rect- angle contained by the extremes is equal to the square on the mean : and conversely . Page 164

If the four straight lines a , b , c , d are

If the four straight lines a , b , c , d are

**proportional**, then a cas b ; d . For a bas c : d ; ... rect . ( a , d ) = rect . ( b , c ) ; .. a : c as b : d . PROPOSITION VII . If a b as c : d , then ba as d : c . For rect . Page 167

Also all the preceding theorems may be similarly ex- tended to other magnitudes as solids and angles . For solids may be shewn to be

Also all the preceding theorems may be similarly ex- tended to other magnitudes as solids and angles . For solids may be shewn to be

**proportional**to certain straight lines and angles to certain arcs . Moreover PROPOSITION XIII .### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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.