## Euclidian Geometry |

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Side v

... required by the Universities have been established and at the same time

Problems separated from Theorems , both classified according to the nature of

the subject , and demonstrations replaced by others

careful ...

... required by the Universities have been established and at the same time

Problems separated from Theorems , both classified according to the nature of

the subject , and demonstrations replaced by others

**less**cumbrous , I have beencareful ...

Side xv

place before the student the various steps of an argument in a more succinct form

by curtailing the verbiage , thus enabling him to take in at a glance the outline of

a ...

**less**than . . : : because . . : therefore . : is to . The object aimed at is merely toplace before the student the various steps of an argument in a more succinct form

by curtailing the verbiage , thus enabling him to take in at a glance the outline of

a ...

Side 2

The size of an angle does not depend on the length of its arms but on their

direction , and is said to be greater or

of its arms is greater or

enclose a ...

The size of an angle does not depend on the length of its arms but on their

direction , and is said to be greater or

**less**according as the difference of directionof its arms is greater or

**less**. . . It is evident that Two straight lines - cannotenclose a ...

Side 23

Hence it follows that Any two angles of a triangle are together

angles . Let ABC be a a . Then shall any two of its angles , as ABC and ACB , be

together < two right angles . Produce BC to D . Then LABC is < the exterior 4ACD

...

Hence it follows that Any two angles of a triangle are together

**less**than two rightangles . Let ABC be a a . Then shall any two of its angles , as ABC and ACB , be

together < two right angles . Produce BC to D . Then LABC is < the exterior 4ACD

...

Side 27

If from the ends of one of the sides of a triangle there be drawn two straight lines

to a point within the triangle : these shall be

triangle but shall contain a greater angle . B From the ends B , C of the side BC of

...

If from the ends of one of the sides of a triangle there be drawn two straight lines

to a point within the triangle : these shall be

**less**than the other two sides of thetriangle but shall contain a greater angle . B From the ends B , C of the side BC of

...

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base bisect Cambridge centre chapter chord circle circumference 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 rect rectangle render respectively revised right angles Schools segment selected sides similar Similarly square taken tangent THEOREM third touch TREATISE triangle twice University volume whole

### Populære avsnitt

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

Side 26 - 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.

Side 58 - 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.

Side 47 - HISTORICAL OUTLINES OF ENGLISH ACCIDENCE, comprising Chapters on the History and Development of the Language, and on Word-formation.

Side 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.

Side 63 - 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.

Side 61 - 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.

Side 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.

Side 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...

Side 31 - ... 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.