Class lessons on Euclid1882 |
From inside the book
Results 1-5 of 43
Page 17
... construct a mathematical figure . Def . 24 tells us that an equilateral triangle is a figure having three equal sides . The given line will itself form one side of the triangle , and if we can draw two other lines equal to it in such a ...
... construct a mathematical figure . Def . 24 tells us that an equilateral triangle is a figure having three equal sides . The given line will itself form one side of the triangle , and if we can draw two other lines equal to it in such a ...
Page 25
... constructing the triangles we must do what we can to make them equal , so let us take point G , so that CG ( a side ... constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each ...
... constructing the triangles we must do what we can to make them equal , so let us take point G , so that CG ( a side ... constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each ...
Page 31
... construct two isosceles triangles , with a common base CD . What do we know further about these triangles ? Because they are isosceles the angles at their bases are equal , i.e. Angle ( 1 ) ACD = angle ( 2 ) ADC . " " ( 3 ) BCD = 99 ( 4 ) ...
... construct two isosceles triangles , with a common base CD . What do we know further about these triangles ? Because they are isosceles the angles at their bases are equal , i.e. Angle ( 1 ) ACD = angle ( 2 ) ADC . " " ( 3 ) BCD = 99 ( 4 ) ...
Page 35
... construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must fulfil the conditions either of I. 4 or of I. 8. As we have no angles given equal , we must follow I. 8 and endeavour to construct ...
... construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must fulfil the conditions either of I. 4 or of I. 8. As we have no angles given equal , we must follow I. 8 and endeavour to construct ...
Page 46
... constructed satisfy the conditions of I. 4 , and are therefore equal . Next , can we retrace our steps , and construct these equal triangles , without assuming angle ECX ? We can , as before , bisect AC in E , thus obtaining AE equal to ...
... constructed satisfy the conditions of I. 4 , and are therefore equal . Next , can we retrace our steps , and construct these equal triangles , without assuming angle ECX ? We can , as before , bisect AC in E , thus obtaining AE equal to ...
Other editions - View all
Common terms and phrases
&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
Popular passages
Page 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
Page 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.
Page 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.
Page 10 - HAWEIS, Rev. HR, MA— Current Coin. Materialism— The Devil — Crime — Drunkenness — Pauperism — Emotion — Recreation —The Sabbath.
Page 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.
Page 17 - The Christian Year. Thoughts in Verse for the Sundays and Holy Days throughout the Year.
Page 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.
Page 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,
Page 6 - The Doctrine of Last Things contained in the New Testament compared with the Notions of the Jews and the Statements of Church Creeds.
Page 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.