 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, which are placed in separate consecutive paragraphs, which paragraphs...  Library of Useful Knowledge: Mathematics I. - Side 691836Uten tilgangsbegrensning - Om denne boken
 | Robert Gibson - 1806 - 486 sider
...for it has been 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 parallel0gram ABDC... | |
 | Robert Gibson - 1808 - 482 sider
...j for it has been proved that ABCD being a parallelogram, AB will be=CD and AD=BC. THEO. XIII. All parallelograms on the same or equal bases and between the same parallels, are equal to one another, that is, ifBD=GH, and the lines Ell and AY parallel, then the parallelogram ABDC=BDFE=EFHG.... | |
 | Robert Gibson - 1811 - 580 sider
...|»rallelogram E FG H= B DEF. Wherefore ABDC=> BDEF=EFHG. 3. ED Cor. Hence it is plain that triangles on the same or equal bases, and between the same parallels, are equal, seoing (by cor. 2. theo. 1Q.) theyavf the halves of their respective parallelogram • THEO. XIV. PL.... | |
 | Robert Gibson - 1814 - 558 sider
...the parallelogram EFGH=BDEF. Wherefore ABDC=BDEF=EFHG. QED ч Cor. Hence it is plain that triangles on the same or equal bases, and between the same parallels, are equal, seeing (by cor. 2. theo. 12.) they are the halves of their respective parallelogram. THEO. XIV. PL.... | |
 | Robert Gibson - 1818 - 502 sider
...for it has been 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.... | |
 | Nathaniel Bowditch - 1826 - 764 sider
...For it has been proved, that ABDC being a parallelogram, AB is equal to CD, and AC equal to BD. L* AU parallelograms on the same or equal bases, and between the same parallels, an equal to each other ; that is, if BD and GH be equal, and the lines BH, AF be parallel, the parallelograms... | |
 | Pierce Morton - 1830 - 584 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... | |
 | Augustus De Morgan - 1831 - 108 sider
...Here refer to the necessary problems. If two lines be drawn at right angles to two others, the angles made by the first and second pair are equal. All right...second column on the left we state the reasons for each paragraph, either by referring to the preceding paragraphs from which they follow, or the preceding... | |
 | Robert Gibson - 1832 - 290 sider
...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 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.... | |
 | Robert Mudie - 1836 - 524 sider
...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,... | |
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