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" If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight... "
First principles of Euclid: an introduction to the study of the first book ... - Σελίδα 104
των T S. Taylor - 1880
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 σελίδες
...third angle BAC to the third angle EDF. Wherefore if two triangles, &c. QED PROPOSITION XXVII. THEOREM. If a straight line, falling on two other straight lines, make the alternate angles equal to each other ; these two straight lines shall be parallel. Let the straight...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 σελίδες
...C ; .'. AB || CD ; ™. ss. GEOMETRY. PROP. XXVII. THEOR. 28. 1 Eu. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line; or make the interior angles upon the same side together equal to two...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 σελίδες
...meet towards A, C ; .-. AB || CD; Def. 35PROP. XXVII. THEOR. 28. 1 Eu. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line; or make the interior angles upon the same side together equal to two...

Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 166 σελίδες
...two straight lines (AB, CD), make equal the exterior angle (EGB) to the interior opposite angle (GHD on the same side of the line ; or make the interior angles (BGH, GHD) equal to two right angles, the two lines shall be parallel. Argument 1. Since, by hyp. EGB...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...these two straight lines shall be parallel. PROP. XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two...

The English Journal of Education, Τόμος 4

1850 - 488 σελίδες
...greater than cither of the interior opposite angles. SECTION II. 1. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two...

Papers for the schoolmaster, Τόμος 3

1867 - 336 σελίδες
...which are opposite to the less of the two sides. Are such triangles necessarily equal? SSOTION III. 1. If a straight line, falling on two other straight lines, make the alternate angles equal to one another; these two straight lines slmll be parallel. Two triangles ABC,...

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

Euclides - 1853 - 146 σελίδες
...to CD. Wherefore if a straight line, &c. QED PROP. XXVIII. THEOREM. If a straight line falling upon two other straight lines make the exterior angle equal to the interior and opposite upon the same side of the line; or make the interior angles upon the same side together equal to two...

The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Βιβλίο 1

Euclides - 1853 - 334 σελίδες
...angles BGH, GHC are equal. Which was to be proved. II. Any one of the exterior angles, EGB, shall be equal to the interior and opposite angle on the same side of EF, viz. GHD. The angle EGB is equal to the angle AGH, since they are opposite vertical angles (i....

The popular educator, Τόμος 4;Τόμος 7

Popular educator - 1852 - 1272 σελίδες
...straight lines AB and o D are parallel. QED PROPOSITION XXVIII.*-THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite angle upon the lame side of the straight line ; or make the two interior angles upon the tame side of it,...




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