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Bøker Bok 110 av 30XIII. •All parallelograms on the same or equal bases and between the same parallels...
" XIII. •All parallelograms on the same or equal bases and between the same parallels... "
A Treatise of Practical Surveying, ... - Side 36
av Robert Gibson - 1808 - 440 sider
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 452 sider
...ABCD— BDEF ; in like manner we may prove the parallelogram EFGH = BDEF. Wherefore ABDC=BDEF=EFGH. QED Cor. Hence it is plain that triangles on the same or equal bases, artd between the same parallels, are equal, seeing (by cor 2. theo. 12.) they are the halves of their...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 sider
...BDEF ; in like manner we may prove the |»rallelogram E FG H= B DEF. Wherefore ABDC=> BDEF=EFHG. 3. ED Cor. Hence it is plain that triangles on the same...bases, and between the same parallels, are equal, seoing (by cor. 2. theo. 1Q.) theyavf the halves of their respective parallelogram • THEO. XIV. PL....
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1814 - 508 sider
...ABCD=BDEF ; in like manner we may prove the parallelogram EFGH=BDEF. Wherefore ABDC=BDEF=EFHG. QED ч Cor. Hence it is plain that triangles on the same...theo. 12.) they are the halves of their respective parallelogram. THEO. XIV. PL. \,ßg. 32. In every right-angled triangle, ЛВС, the square of the...
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A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1818 - 478 sider
...proved that ABCD being a parallelogram, AB will be=CD and AD=BC. THEOREM XIII. •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 parallel, then the parallelogram J1BDC=BDFE=EFHG....
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1821 - 544 sider
...being a 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.=...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...its base and altitude . cor. 16 •и two Greek words, signifying " along one (i) Parallelograms upon the same or equal bases, and between the same parallels, are equal to one another 16 (A) If a parallelogram and a triangle stand upon thesarae base, and between the same...
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On the study and difficulties of mathematics [by A. De Morgan].

Augustus De Morgan - 1831
...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 sider
...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 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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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...
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Library of Useful Knowledge: On the study and difficulties of mathematics ...

1836
...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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