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" Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. "
An essay on mechanical geometry, explanatory of a set of models - Page 11
by Benjamin Donne - 1796
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...doubles of the same thing, are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide with one another (that is to say, which fit together so exactly that every point of the one lies on some point of the other)...
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Elements of Mental Philosophy Enbracing the Two Departments of the ..., Volume 1

Thomas Cogswell Upham - Intellect - 1841 - 474 pages
...the same are equal to one another ; Things which are halves of the same are equal to one another ; Magnitudes which coincide with one another (that is, which exactly fill the same space) are equal to one another, &c. It will be admitted (and we shall see it perhaps more clearly...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...are equal to one another. VII. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines...
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Chambers's Information for the People, Volume 2

William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...Things which are double of the same, are equal to one another. 7. Things which are halves of the came, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...doubles of the same thing, are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...fact, merely what a logician would call the converse of it; for in the 8th axiom it is stated, that magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another ; and in this theorem, in order to prove them equal, it is proved...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...are equal to one another. VII. Things which are halves of the same are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. NB. The term ' equivalent' is used in this work to denote equality...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...doubles of the same thing, are equal to one another. 7. Things which are halves of the same thing, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. All right angles are...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...or equal things, are equal to one another. 7- Things which are halves of the same, or equal things, are equal to one another. 8. Magnitudes which coincide...with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part, aud equal to all its parts...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...are equal to one another. vn. Things which are halves of the same, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX. The whole is greater than its part. X. Two straight lines...
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