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" Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1900
...triangle, it will cut the other sides (or the other sides produced) proportionately. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. ABC is a triangle right angled at A, D is the midpoint of EG, and AE. EF are drawn perpendicular to...
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THE CONTENTS OF THE FIFTH AND SIXTH BOOKS OF EUCLID

M. J. M. HILL - 1900
...— E : F, where all the magnitudes are of the same kind, then A :B=A + C+E:B+D + F. 44. The areas of similar rectilineal figures are to one another in the duplicate ratio of corresponding sides. 45. (i) If'A:JB=C:D, then figure on A : similar and similarly described figure...
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Sessional Papers, Volum 22,Del 2

Great Britain. Parliament. House of Commons - 1900
...described with 0 as centre and OM as radius, then AM will bisect the angle PAQ. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. RUGBY SCHOOL SCHOLARSHIP EXAMINATION. — June, 1899. ALGEBRA. 1. Find the square root of the expression...
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Calendar

University of Sydney - 1901
...one minute. 7. Triangles of the same altitude are to one another as their bases. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. 0. Find the diameter of a cylindrical pipe, two feet long, containing a volume of 000 cubic inches....
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Manual

1903
...straight line bisecting the angle E makes equal angles with AB and CD. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Or, 6A. Prove that if two chords of a circle intersect either within or without the circle, the rectangle...
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The Possibility of a Science of Education

Samuel Bower Sinclair - 1903 - 126 sider
...the preposition is superior to the former method is as true as the statement that "similar triangles are to one another in the duplicate ratio of their homologous sides." And yet notwithstanding all this there are many good teachers who are vigorously opposed to all study...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...of similar triangles, having the same ratio each to each that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. H Let ABCDE, FGHKL be similar polygons, and let AB and FG be homologous sides. Then (i) the polygons...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908
...remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles....
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Books 3-9

Euclid - 1908
...i0 corresponding sides. And it was also proved in the case of triangles ; therefore also, generally, similar rectilineal figures are to one another in the duplicate ratio of the corresponding sides. QED 2. in the same ratio as the wholes. The same word fyiiXo-yos is used which...
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English Mechanic and World of Science: With which are Incorporated ..., Volum 28

1879
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures are to one another in the duplicate ratio of their homologous sides" — that is, that these figures — meaning the areas of them— are to one another as the squares...
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