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" Any two sides of a triangle are together greater than the third side. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Σελίδα 72
των Thomas Perronet Thompson - 1833 - 150 σελίδες
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...is not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 10. (Eue. L 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...angle of every triangle is subtended by the greater side, or has the greater side opposite to it. XX. Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one side of a triangle, there be drawn two straight lines to a point within...

A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 σελίδες
...than BAC, by preceding ART. ; which it is not. Hence BA must be greater than BC. This, &c. ART. 43. Any two sides of a triangle are together greater than the third tide. In the triangle ABC, any two of its sides, as AB, BC, are together greater than the third side...

Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - 1836 - 220 σελίδες
...be less than С ; wherefore the side A С must be greater than the side A B. THEOREM IV. 35. Aпу two sides of a triangle are together greater than the third side. А с Any two sides AB, B С of the triangle ABС, are together greater than the third side A С. In...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...less than AB ; and it has been shown that it is not equal to AB ; therefore AC is greater than AB. PROPOSITION XX. THEOREM. Any two sides of a triangle...third side. Let ABC be a triangle ; any two sides of it together are greater than the third side; namely, the sides BA, AC, greater than the side BC ; and...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...Demonstration. 1. Prove that AC cannot be = AB, 2. that AC cannot be < AB, 3. that :. AC must be > AB. PROPOSITION XX. Theorem. Any two sides of a triangle are together greater than the third. BC Steps of the Demonstration. 1. Prove that Z ADC = Z ACD, 2. that Z BCD > Z ACD, 3. that .'. DB >...

Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

C. Reiner - 1837 - 215 σελίδες
...to the greater angle. 13. In every triangle the greater angle is subtended by the greater side. 14. Any two sides of a triangle are together greater than the third side. 15. The difference between any two sides of a triangle is less than the third side. 16. The three sides...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 σελίδες
...is not equal toAB: therefore AC is greater than A B. Wherefore, if two angles, &c. PROP. XX. THEOR. ANY two sides of a triangle are together greater than the third side. 8 Let ABC be a triangle ; any two sides of it are together greater than the third side. Produce (I....

Ward's miscellany (and family magazine).

1837
...without knowing it — both theoretical and practical. A mathematician sits down to demonstrate that the two sides of a triangle are together greater than the third side ; whereas, without any of the diagrams, anil ABC's, and f/uo(l trat demonstrandus of Euclid, a poi...

Lessons on form; or, Introduction to geometry as given in a Pestalozzian ...

Charles Reiner - 1837
...of the preceding truths will guide you ? P.—" The greater side subtends the greater angle;" or, " any two sides of a triangle are together greater than the third." M.—If you adopt the former of these truths, how must you draw a line so as to find a relation between...




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