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If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Σελίδα 273
των John Playfair - 1855 - 318 σελίδες
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## Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 σελίδες
...Note.— The converse of this proposition, that "if a straight line meeting two other straight lines make the two interior angles on the same side of it taken together less than two right angles, the two lines will, if produced tar enough) meet on that Bide on which are the angles less than two...

## An introduction to geometry, consisting of Euclid's Elements, book ..., Τόμος 1

Euclides - 1884 - 182 σελίδες
...to discuss it until we have made some further progress in the subject. 12. If a straight line meet two straight lines so as to make the two interior...together less than two right angles, these straight lines,being continually produced, shall at length meet on that side on which are the angles which are...

## The national encyclopædia. Libr. ed, Τόμος 2

National cyclopaedia - 1884 - 642 σελίδες
...as stated by Euclid it is not a true axiom. It runs thus — 44 If a straight line meets two other straight lines, so as to make the two interior angles on the same side of it, taken j together, less than two right angles ; these straight lines, being continually produced, shall at...

## A Short History of Greek Mathematics

James Gow - 1884 - 350 σελίδες
...straight lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so as to make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side. Of these...

## Mathematical Questions and Solutions, Τόμος 42

1885 - 150 σελίδες
...would coincide with EF ; and thus is it proved that all right angles are equal.* Axiom XII.: — " If a straight line meets two straight lines, so as...together, less than two right angles, these straight linos being continually produced, shall at length meet upon that side on which are the angles which...

## Transactions and Proceedings of the New Zealand Institute, Τόμος 18

New Zealand Institute - 1886 - 530 σελίδες
...equivalence of the three forms of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight lines, so as to make the two interior angles on the same I side of it taken together less than two right angles, these straight lines being continually produced...

## A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - 518 σελίδες
...so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together less than two...lines being continually produced shall at length meet on that side< on which are the angles which are less than, two right angles. An axiom must possess...

## The Teaching and History of Mathematics in the United States

Florian Cajori - 1890 - 412 σελίδες
...consists in what is generally called the twelfth, by some the eleventh "axiom :" " If a straight line meet two straight lines so as to make the two interior...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...

## Circular of Information of the Bureau of Education, for ..., Τεύχη 1-3

United States. Office of Education - 1890 - 958 σελίδες
...in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines so as to make the two interior...on the same side of it taken together less than two right-angles, these straight lines, being continually produced, shall at length meet on that side on...

## The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...— Prove this proposition independently of Prop. 27. Ax. 12. — If a straight line meet two other straight lines so as to make the two interior angles on the same side of it together less than two right angles, these two straight lines being continually produced shall at length...