Class lessons on Euclid1882 |
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Σελίδα 46
... exterior angle ACD shall be greater than either of the interior and opposite angles CBA , BAC . The construction made use of by Euclid for the proof of this theorem is exceedingly ingenious . We may imagine that it was arrived at in ...
... exterior angle ACD shall be greater than either of the interior and opposite angles CBA , BAC . The construction made use of by Euclid for the proof of this theorem is exceedingly ingenious . We may imagine that it was arrived at in ...
Σελίδα 47
... exterior angle ACD is greater than either of the interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater than either of the interior and opposite angles . I. To show that ...
... exterior angle ACD is greater than either of the interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater than either of the interior and opposite angles . I. To show that ...
Σελίδα 48
... exterior angle , together with the adjacent interior angle , are equal to two right angles ( I. 13 ) . Produce BC , the base of triangle ABC , to D , then angles ACD , ACB are to- gether equal to two right angles . Now we know that ...
... exterior angle , together with the adjacent interior angle , are equal to two right angles ( I. 13 ) . Produce BC , the base of triangle ABC , to D , then angles ACD , ACB are to- gether equal to two right angles . Now we know that ...
Σελίδα 49
... exterior angle of the triangle DBC , and is therefore greater than the interior and opposite angle ACB . Then angle ADB is less than angle ABC and greater than angle ACB , ' much more then must angle ABC be greater than angle ACB . ' E ...
... exterior angle of the triangle DBC , and is therefore greater than the interior and opposite angle ACB . Then angle ADB is less than angle ABC and greater than angle ACB , ' much more then must angle ABC be greater than angle ACB . ' E ...
Σελίδα 53
... exterior angle of a triangle , of which the other is an interior and opposite angle ( I. 16 ) . The latter condition will be the most likely to help us here . amining the figure you will see Ex- B angle BDC is greater than △ BEC ( I ...
... exterior angle of a triangle , of which the other is an interior and opposite angle ( I. 16 ) . The latter condition will be the most likely to help us here . amining the figure you will see Ex- B angle BDC is greater than △ BEC ( I ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
&c.-Q.E.D. PROPOSITION ABCD alternate angles angle ABC angle ACB angles are equal angles equal base BC bisected Cheaper Edition circle cons construction Demy 8vo diameter enunciation equal bases equal in area equal sides equal triangles equilateral triangle Euclid exterior Fcap Frontispiece given angle given line given point given straight line given triangle gnomon gram half the line Illustrations interior and opposite interior angles isosceles triangle Join line equal meet opposite angles opposite sides parallelogram perpendicular Poems problem produced proof Prop rectangle contained rhombus right angles right-angled triangle Second Edition sides equal Small crown 8vo square on AC square on half SUMMARY OF PROPOSITION THEOREM Third Edition Translated triangle ABC triangles are equal twice the rect twice the rectangle vertical angle vols Wherefore whole line
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Σελίδα 25 - THE INTERNATIONAL SCIENTIFIC SERIES. I. Forms of Water : a Familiar Exposition of the Origin and Phenomena of Glaciers. By J. Tyndall, LL.D., FRS With 25 Illustrations. Eighth Edition. Crown Svo, 5*. II. Physics and Politics ; or, Thoughts on the Application of the Principles of "Natural Selection " and " Inheritance
Σελίδα 19 - Ezra, Nehemiah, and Esther. By Rev. Canon G. RAWLINSON, MA With Homilies by Rev. Prof. JR THOMSON, MA, Rev. Prof. RA REDFORD, LL.B., MA, Rev. WS LEWIS, MA, Rev. JA MACDONALD, Rev. A. MACKENNAL, BA, Rev. W. CLARKSON, BA, Rev. F. HASTINGS, Rev. W. DINWIDDIE, LL.B., Rev. Prof. ROWLANDS, BA, Rev. G. WOOD, BA, Rev. Prof. PC BARKER, MA, LL.B., and the Rev.
Σελίδα 14 - The Medical Guide for Anglo-Indians. Being a Compendium of Advice to Europeans in India, relating to the Preservation and Regulation of Health. With a Supplement on the Management of Children in India. Second Edition. Crown 8vo. Limp cloth, price 3* . 6d, MALDEN (HE and EE) Princes and Princesses.
Σελίδα 10 - HAWEIS, Rev. HR, MA— Current Coin. Materialism— The Devil — Crime — Drunkenness — Pauperism — Emotion — Recreation —The Sabbath.
Σελίδα 30 - WARTENSLEBEN (Count H. von). The Operations of the South Army in January and February, 1871. Compiled from the Official War Documents of the Head-quarters of the Southern Army. Translated by Colonel CH von Wright. With Maps. Demy 8vo.
Σελίδα 17 - The Christian Year. Thoughts in Verse for the Sundays and Holy Days throughout the Year.
Σελίδα 22 - Church and Home. Selected and Edited by the Rev. W. Fleming Stevenson. The most complete Hymn Book published. The Hymn Book consists of Three Parts : — I. For Public Worship. — II. For Family and Private Worship. —III. For Children. %* Published in various forms and prices, the latter ranging from 8d.
Σελίδα 25 - YOUMANS (Eliza A.). An Essay on the Culture of the Observing Powers of Children, especially in connection with the Study of Botany. Edited, with Notes and a Supplement, by Joseph Payne, FCP, Author of " Lectures on the Science and Art of Education,
Σελίδα 6 - The Doctrine of Last Things contained in the New Testament compared with the Notions of the Jews and the Statements of Church Creeds.
Σελίδα 5 - A General History of Greece from the Earliest Period to the Death of Alexander the Great, with a sketch of the subsequent History to the present time. New Edition. Crown 8vo. Cloth, price 7*. 6d. Tales of Ancient Greece.