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" Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Σελίδα 10
των Euclides - 1852
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 σελίδες
...means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added...

The New quarterly review, and digest of current literature, Τόμος 7

1858 - 422 σελίδες
...have a gayer or gladder aspect. Mr. Smith's only justification here is a mathematical one : that as things which are equal to the same are equal to one another, and both blossoms and tears have been likened to a shower of rain, therefore blossoms may always be...

The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 σελίδες
...compasses. Having these, the reader will be able to draw any of the figures in this book.] AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders...

The British Millennial Harbinger

1852 - 588 σελίδες
..."Yes." " And the three baskets three days too?" "Yes." Well, thought I, if it be a true axiom that things which are equal to the same are equal to one another, then a grape vine and a basket are identical ! So, finding the rabbinical logic of this poor deluded...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 σελίδες
...But it has been proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things which are equal to the same are equal to one another (Ax. 1.) ; therefore 3. CA is equal to CB. Wherefore CA, AB, BC, are equal to one another ; and therefore...

An introduction to mental philosophy

sir George Ramsay (9th bart.) - 1853 - 282 σελίδες
...intervention of any general axiom, that the side AB is equal to the side A C. The general axiom, that things which are equal to the same are equal to one another, cannot make the conclusion one whit more evident than it was before. We see at once from the particular...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 σελίδες
...but it has been proved that ca is equal to ab; therefore ca, cb, are each of them equal to ab ; but things which are equal to the same are equal to one another (1 ax.); therefore ca is equal to cb; wherefore ca, ab, bc are equal to one another; and the triangle...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB : But things which are equal to the same are equal to one another (1 Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, BC are equal to one another; and the triangle...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 σελίδες
...means the square•root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added...

The Principles of animal and vegetable physiology

J. Stevenson Bushnan - 1854 - 268 σελίδες
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another; that twice four are...




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