 | 1867 - 964 σελίδες
...any point in tho straight line HK, produced both ways indefinitely. Triangles also which stand npon equal bases and between the same parallels are equal to one another. Thus, the triangles LNG, M o F, which „ ._ stand on equal bases, NG, F o, and K between the same... | |
 | Robert Gibson - 1795 - 384 σελίδες
...will be = CD and AD=BC. THEO. Xin. All Parallelograms on the fame or equal Safes and letween the fame Parallels are equal to one another , that is if BD=GH, and the Linet BH and AF parallel, then the Parallelogram ABDC=BDFE=EFHG. For AC (=DB=EF (by Cor. the laft)... | |
 | Robert Gibson - 1806 - 486 σελίδες
...; 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...another, that is, if BD^GH, and the lines BH and AF parallel, then the parallel0gram ABDC ^BDFE=EFHG. .fig. 31. For AC=BD=EF (by cor. the last ;) to both... | |
 | Robert Simson - 1806 - 546 σελίδες
...is'equal to the triangle DBC. Wherefore, triangles, fee, QE D, 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... | |
 | John Playfair - 1806 - 320 σελίδες
...EBCF. Therefore, parallelograms upon the same base, &c. QED PROP. XXXVI. THEOR. PARALLELOGRAMS upon equal bases, and between the same parallels, are equal to one another. Let ABCD, EFGH be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG; the... | |
 | Robert Gibson - 1808 - 482 σελίδες
...the parallelogram EFGH=BDEF. Wherefore ABDC=BDEF=EFHG. QED " 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 parallelograms. THEO. XIV. In... | |
 | Robert Gibson - 1811 - 580 σελίδες
...|»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.... | |
 | John Mason Good - 1813 - 714 σελίδες
...base, and between the same parallels, are equal to one another. Prop. XXXVIII. Theor. Triangles upon equal bases, and between the same parallels, are equal to one another. Prop. XXXIX. Theor. Equal triangles upon the same base, and upon the same side of it, are between the... | |
 | Euclides - 1816 - 588 σελίδες
...Therefore parallelograms upon the same base, &c. QED 1 PROP. XXXVI. THEOR. Boot I. PARALLELOGRAMS upon equal bases, and between the same parallels, are equal to one another. •f> K LetABCD,EFGH,be parallelograms upon equal bases BC,FG, and between the same parallels AH, BG;... | |
 | Robert Gibson - 1818 - 502 σελίδες
...prove the parallelogram EFGH=BDEF. Wherefore ABCD=BDEF=EFHG. QED 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 parallelograms. THEOREM XIV.... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
