Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other... "
Elements of Geometry: With Practical Applications ... - Page 22
by George Roberts Perkins - 1847 - 308 pages
Full view - About this book

Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...and join GH. fa/ V Then the triangles GBH, DEF are equal, since two sides and the included angle in the one are respectively equal to two sides and the included angle in the other ; hence, and by hypothesis, AB : BC : : GB : BH, that is, the sides BA, BC of the triangle...
Full view - About this book

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Demonstration. In the two triangles ABC, DJP(ng.31), let the angle A be equal to the...
Full view - About this book

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

Euclid - Geometry - 1837 - 410 pages
...respect equal. They are proved to be such in the fourth proposition, u In , tivo sides and the contaHied angle of the one are respectively equal to two sides and the contained angle of the other : in the eighth, when the three sides of the one are equal to the three...
Full view - About this book

Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...consequently they are equal. (Ax. 13.) Hence, universally, Any two triangles are every way equal, when two sides and the included angle of the one, are respectively equal to two sides and the included angle of the other. PROPOSITION VI. THEOREM. If two triangles ABC, DEF, have two angles and the interjacent...
Full view - About this book

Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...has been proved (Prop. VIII.) that two triangles are equal, when two sides and the included angle in the one, are respectively equal to two sides and the included angle in the oilier ; we may now infer further, that two triangles are equivalent or equal in surface, when...
Full view - About this book

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

Euclid, James Thomson - Geometry - 1845 - 382 pages
...respect equal. They are proved to be such in the fourth proposition, when two sides and the contained angle of the one are respectively equal to two sides and the contained angle of the other: in the eighth, when the three sides of the one are equal to the three...
Full view - About this book

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...the equal angles in the second, are called homologous. 51. Theorem. Two triangles are equal, when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Proof. In the two triangles ABC, DEF, (fig. 31), let the angle Jl be equal to the angle...
Full view - About this book

Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...and a increase or decrease together. Cor. 2. Two spherical triangles are equal : (537) 1. When two sides and the included angle of the one are respectively equal to the two sides and the included angle of the other ; and therefore, FOR A SIDE. 265 Fig. 120a. 2....
Full view - About this book

Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...to DF, and join GH. Then the triangles AGH, DEF are equal, since two sides and the included angle in the one, are respectively equal to two sides and the included angle in the other (Prop. VI., BI). But, by hypothesis, AB : DE : : AC : DF; therefore AB : AG : : AC : AH;...
Full view - About this book

Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...than CB ; then take AD equal to BC, and join DJB. Now, in the two triangles DAB and CBA, we have ^ A equal to CB by construction, the side AB common, and...CB and CA, and therefore the triangle is isosceles. 'IPROPOSITION VIII. .THEOREM. When two triangles have the three sides of the one respectively equal...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF