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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Σελίδα 26
των Dennis M'Curdy - 1846 - 138 σελίδες
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1821 - 544 σελίδες
...parallelogram, AB will be = CD and AD ~ BC. THEO. XIII. PL. I. Jig. 31. All parallelograma on the same or equal bases and between the same parallels, are equal to one another, that is, if BD = GH, and the lines £H and AF parallel, then the paralleloe-ram JIBDC=,BDFE.= EfHG....

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...is equal to the triangle DBC. Wherefore triangles, &c. QED Propoíiíion XXXVIII. Theorem. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...the triangle DBC. Therefore triangles, &c. QED PROPOSITION XXXVIII. THEOREM. Triangles constituted upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DCE, be constituted upon equal bases вс, CE, and <? A n н between the same parallels...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...the same parallels вс, EF. And the triangle PROPOSITION XXXVIII. THEOREM. , Triangles constituted upon equal bases, and between the same parallels, are equal to one another. * si.i. rallel to сл; " also through E draw EH B c E Let the triangles ABC, DCE, be constituted upon...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...to the parallelogram EBCF. Therefore parallelograms upon the same base, &c. QED PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let ABC^DjEFGH, be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG: the parallelogram...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 σελίδες
...(Prop. 34.), and therefore are equal to one another. ED. PROPOSITION XXXVIII. THEOREM. Triangles on equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be on equal bases BC, EF, and between the same parallels BF, AD; the triangle...

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 σελίδες
...triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. QED PROP. XXXVIII. THEOR. TRIANGLES upon equal bases, and between the same parallels, are equal to one auother. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF,...

First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - 1830 - 12 σελίδες
...to perceive, that the magnitude of an angle does not depend upon the greatneii 12* 128 GEOMETRY. 5. Parallelograms upon equal bases and between the same parallels are equal to one another. 6. The area of a parallelogram is found by multiplying the basis given in rods, feet inches, &c. by...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 σελίδες
.... AF the «ce» above tbe side В С, • ' t GEOMETRY. (с) Triangles which stand upon the same or upon equal bases, and between the same parallels, are equal to one another • . . . -17 (rf) Triangles which have equal altitudes are tourne another as their bases, and triangles...

The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1832 - 348 σελίδες
...parallelogram, AB will be = CD, and AD=BC. THEOREM XIII. PL. l.fig.3l All parallelograms on the same or equal bases and between the same parallels are equal to one another ; that is, if BD=GH, and the lines BH and AF are parallel, then &e parallelogram ABDC—BDFE—EFHG....




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