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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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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 σελίδες
...triangles 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. The...

An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Μέρος 1

Francis Joseph Grund - 1834 - 190 σελίδες
...4. The areas of all parallelograms, which have equal bases and heights, are equal to one another. 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.,...

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

Euclid - 1835 - 513 σελίδες
...equal 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 triangle...

Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...the same base and altitude. PROP. 27. (Eue. i. 37, 38, 39, & 40.) Triangles upon the same base, or upon equal bases, and between the same parallels, are equal to one another : and conversely, equal triangles, upon the same base, or upon equal bases in the same straight line,...

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

1836 - 472 σελίδες
...Parallelograms upon the same base and between the same parallels, are equal to one another. XXXVI. Parallelograms upon equal bases, and between the same parallels, are equal to one another. XXXVII. Triangles upon, the same base, and between the same parallels, are equal to one another. XXXVIII....

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

Euclid, James Thomson - 1837 - 390 σελίδες
...parallelogram AC is equal to the parallelogram BF.* Therefore parallelograms, &c. PROP. XXXVI. THEOR. PARALLELOGRAMS upon equal bases, and between the same parallels, are equal to one another. Let AC, EG be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG; the parallelogram...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...7) ; therefore the triangle ABC is equal to the triangle DBC. PROPOSITION XXXVm. 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...

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

Euclid, Robert Simson - 1838 - 416 σελίδες
...is, the he parallelogram EBCF. Therebase, &c. Q,. ED See the 2d and 3d figures. D PROP. XXXVI. THEOR. PARALLELOGRAMS upon equal bases, and between the same...parallels, are equal to one another. Let ABCD, EFGH be pa- A rallelograms upon equal bases BC, FG, and between the same parallels AH, BG; the parallelogram...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...that cannot be suppressed, because it helps to prove the general case. PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon eqnal bases BC EF, and between the same parallels BF, AD : the triangle...

The Elements of Euclid

Euclid - 1838 - 416 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 another. BOOK I. THE ELEMENTS OF EUCLID. B E between the same parallels BF, AD : the triangle ABC is equal to...




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