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" DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to... "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 8
por Euclides - 1814
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...to the remainder BG; (ax. 3.) but it has been shewn that .BCis equal to BG, wherefore AL and BCaie each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872
...straight line, the adjacent £s so formed are together equal to two right £s. (Prop. XIII.) 2. That things that are equal to the same are equal to one another. (Ax. I.) 3. That if the same quantity be taken from two equal quantities the remainders are equal....
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...equal to the remainder BG; but it has been shown that BC is equal to BG ; wherefore AL and BC are cash of them equal to BG ; and things that are equal to the same are equal to one another ; therefore AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...to BG ; and things which are equal to the same thing are equal to one another (Ax. 1) ; therefore 4. The straight line AL is equal to BC. Wherefore, from...drawn equal to the given straight line BC. Which was to be done. PROPOSITION 3. — Problem. From the greater of two given straight lines to cut off a part...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...are equal to the same thing are equal to one another. [Ax. i.] Therefore AL is equal to BC. Therefore from the given point A a straight line AL has been drawn equal to the given straight line BC. QEF This problem admits of eight cases in the figure. 1. The given point may be joined with either...
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Euclid, Book V Proved Algebraically So Far as it Relates to Commensurable ...

Charles Lutwidge Dodgson - 1874
...are equal to one another. Show that this needs no demonstration . This is an instance of the Axiom " Things, that are equal to the same, are equal to one another." PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent,...
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Euclid, Book V. Proved Algebraically, So Far as it Relates to Commensurable ...

Euclid, Lewis Carroll - 1874 - 62 páginas
...are equal to one another. Show that this needs no demonstration . This is an instance of the Axiom " Things, that are equal to the same, are equal to one another." ~" PROP. XII. If any number of magnitudes be proportionals : as one of the antecedents is to its consequent,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 páginas
...BG, wherefore AL and .BC are each of them equal to BG ; •td things that are equal to the same thing are equal to one another) therefore the straight line AL is equal to BC. (ax. 1.) Wherefore from the given point A, a straight line AL has been drawn equal to the given straight...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877
...are equal to the same thing are equal to one another, therefore AL is equal to BC (Ax. 1). Therefore from the given point A a straight line AL has been...drawn equal to the given straight line BC. Which was to be done. Proposition 3.— Problem. from the greater of two given straight lines to cut off a part...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877
...3) Now AL and BC are each of them equal to BG, therefore AL and BC are equal to each other. (ax. 1) Wherefore from the given point A a straight line AL has been drawn equal to the given straight line. QEF Exercises. 1. If the radms of the smaller circle be half that of the larger, how fails the given...
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