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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
A Treatise on Practical Surveying: Which is Demonstrated from Its First ... - Σελίδα 46
των Robert Gibson - 1818 - 478 σελίδες
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The elements of inductive logic

Thomas Fowler - 1870 - 372 σελίδες
...is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon equal bases, and between the same parallels, are equal to one another,' (2) that 'Triangles formed by the diagonal of a parallelogram are each of them equal to half the parallelogram'...

The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 320 σελίδες
...ABC is equal to the area of the triangle DBC (Bk. IV. Prop. i, Cor.). PROPOSITION 7. Triangles upon equal bases and between the same parallels are equal to one another in area. Let ABC and DEF be two triangles upon the equal bases BC and EF, and between the same parallels...

The Edinburgh university calendar

Edinburgh univ - 1871 - 392 σελίδες
...and 2 doors, each 9 feet by four, with paper I £ yards wide, at 5jd. a yard. 4. Parallelograms upon equal bases and between the same parallels are equal to one another. Prove this ; and modify the enunciation, so as to extend it to the case where the parallelograms are...

Elements of geometry, containing the first two (third and fourth ..., Μέρος 1

Euclides - 1871 - 136 σελίδες
...straight lines, and the lines AD, BC intersect in E, then the triangles AEC, BED are equal. Triangles upon equal bases, and between the same parallels, are equal to one another. Let AS ABC, DEF be on equal bases, BC, EF and between the same IIs BF, AD. Then must A ABC= A DEF....

First book of mathematics

Hugo Reid - 1872 - 146 σελίδες
...ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base and between the same parallels are equal to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels AD and EC....

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...reason thus : Each of the O« is double of &BDC; 1.34. QED PROPOSITION XXXVI. THEOREM. Parallelograms on equal bases, and between the same parallels, are equal to one another. A. J) M !_-. JT Let the Os A BCD, EFGH be on equal bases BC, FG, and between the same II s AH, BG....

Practical Plane and Solid Geometry: For Use in Science Classes and Higher ...

Henry Angel - 1873 - 192 σελίδες
...problems of this chapter. b. Parallelograms (squares, rectangles, and rhomboid figures) or triangles upon the same or equal bases, and between the same parallels, are equal in area (Eviclid, Tk. I., Defs. 35-38). a. The squares on the base and perpendicular of a right-angled...

The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873 - 580 σελίδες
...bisects it ; and DEC is the half of DBCF ; therefore ABC is equal to DEC. XXXVIII. — 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. Produce...

A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 σελίδες
...CB ; shew that the triangle AOD is equal to the triangle BOC. PROPOSITION 38. THEOREM. Triangles on equal bases, and between the same parallels, are equal to one another. . Let the triangles ABC, DEF be on equal bases 1 • BC EF and between the same parallels Bf, AD :...

Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 σελίδες
...consecutive angles of a quadrilateral is half the sum of the two remaining angles. 2. Parallelograms -on equal bases, and between the same parallels, are equal to one another. 3. Divide a given straight line into two parts, so that the rectangle contained by the whole and one...




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