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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 47
των Rev. John Allen - 1822 - 494 σελίδες
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 167 σελίδες
...and XLII, 4.] Proposition 40. 142. Triangles of equal area on equal bases in the same straight line and on the same side of it, are between the same parallels. Let ABC, DEF represent triangles on equal bases BC, EF in the same straight line BF, and on the same...

Euclid's Elements of Geometry, Βιβλία 1-6;Βιβλίο 11

Henry Martyn Taylor - 1895 - 657 σελίδες
...must have one pair and may have two pairs of equal angles. 2. ABC, J)BC are two isosceles triangles on the same base BC, and on the same side of it : shew that AD bisects the vertical angles of the triangles. 3. If the opposite sides of a quadrilateral...

Plane Geometry

George D. Pettee - 1896 - 253 σελίδες
...bisector, and a parallel to the other side, form an isosceles triangle. 76. ABC and DBC are two triangles on the same base BC and on the same side of it, such that ^41? = DC, AC = DB; and AC intersects DB at O. Prove that BOC is isosceles. 77. If a diagonal...

Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 σελίδες
...base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DEC be on the same base BC, and on the same side of it : then they shall be between the same parallels. Construction : Join AD. Proof: AD shall be parallel...

Report of the Committee of Council on Education in Scotland...[without Appendix]

1899
...within the quadrilateral A KCD, prove that BO + CD + DA > PA + РП. 3. Equal triangles on the same base and on the same side of it are between the same parallels. If POQ, ROS are two straight lines through 0, and the triangles POJt, QOS are equal in area, prove...

A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Βιβλίο 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 σελίδες
...means of I. 5) that the angle ABD = the angle ACD. ' 3. ABC, DBC are two isosceles triangles drawn on the same base BC and on the same side of it : employ i. 5 to prove that the angle ABD = the angle ACD. PROPOSITION 7. THEOREM. On the same base,...

Examination Papers

University of Toronto - 1901
...greater than the sum of the diagonals, and less than twice that sum. 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. (I. 39.) If ЛВС and ABD are two equal triangles on the same side of the line AJi ¡aid tiie parallelogram...

Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901
...that the sum of the lines DF, FG, GE has the least possible value. 2. Equal triangles on the same base and on the same side of it are between the same parallels. Use this proposition to show that the straight line joining the middle points of two sides of a triangle...

Annual Report of the Commissioners ..., Τόμος 67

1901
...Inspector. Mr. CUSSEN, District Inspector. SECTION A. 1. Prove that equal triangles on the same base and on the same side of it are between the same parallels. 2. The angles at the base of an isosceles triangle are equal, and if the equal sides be produced, the...

Calendar

University of Sydney - 1902
...side, &c. Complete this enunciation, and prove the proposition. 3. Equal triangles on the same base and on the same side of it are between the same parallels. 4. Straight lines are drawn to bisect the angles at the base BC of an isosceles triangle ABC and to...




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