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Triangles upon equal bases, and between the same parallels, are equal to one another.
A Treatise of Practical Surveying, ... - Pągina 35
per Robert Gibson - 1808 - 440 pągines
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## On the study and difficulties of mathematics [by A. De Morgan].

Augustus De Morgan - 1831
...of one equal to two angles of the others, and the interjacent side equal, are equal in all respects. Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions,...
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## The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1832 - 348 pągines
...been proved that, ABCD being a parallelogram, AB will be = CD, and AD=BC. THEOREM XIII. PL. l.fig.3l All parallelograms on the same or equal bases and...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. For AC=BD=EF...
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## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 pągines
...upon the same base, &c. Which was to be demonstrated. PROPOSITION XXXVIII. THEOREM. — Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon c ADH equal bases BC, EF, and between the same parallels AD, BF....
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## An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - 1834 - 190 pągines
...equal to a rectangle upon the same basis, and of the same height. (Truth I.) 2dly. Parallelograms upon equal bases, and between the same parallels, are equal to one another ; for if they are between the same parallels, their heights must be equal. (Query 11, Sect. I.) 3dly....
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## Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...altitude . cor. 16 • From two Greek words, signifying " along one another.* (i) Parallelograms upon the same or equal bases, and between the same parallels, are equal to one another 16 (/.•) If a parallelogram and a triangle stand upon the same base, and between the same parallels,...
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## The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 pągines
...to the triangle d 7. Ax. DBC. Wherefore, " triangles," &c. QED PROP. XXXVIII. THEOR. 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...
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## Library of Useful Knowledge: On the study and difficulties of mathematics ...

1836
...equal to two angles of the others, and the interjacent side equal, are equal in all respects. /, g Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions,...
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## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 496 pągines
...quantity. This, which is a very useful property, is usually cited in the words, " Parallelograms upon the same or equal bases, and between the same parallels, are equal to each other." But there is some objection to the words " between the same parallels," inasmuch as, to...
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## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 496 pągines
...quantity. This, which is a very useful property, is usually cited in the words, " Parallelograms upon the same or equal bases, and between the same parallels, are equal to each other." But there is some objection to the words "between the same parallels," inasmuch as, to...
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## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 pągines
...upon, the same base, and between the same parallels, are equal to one another. XXXVIII. Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX. Equal triangles upon the same base, and upon the same side of it, are between the same parallels....
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