## Euclidian Geometry |

### From inside the book

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**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 satisfied . PROPOSITION IV ... Page 162

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**proportional**. Then rect . ( a , d ) is = rect . ( b , c ) . On a , b construct rectangles , the altitude of each being equal to c , and on c , d construct rectangles , the altitude of each being equal to a . By hypothesis a b as c : d ... Page 163

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**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 . Hence may be easily established the following Pro- positions : II - 2 ... Page 164

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

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**proportional**to certain straight lines and angles to certain arcs . Moreover PROPOSITION XIII . If A , B , H be areas and c , d , k straight lines , such that A : B as cd , and B : H as d : k , then A : H as c : k . For , if be any ...### Other editions - View all

### 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 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.