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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
The Theory and Practice of Surveying: Containing All the Instructions ... - Σελίδα 52
των Robert Gibson - 1832 - 348 σελίδες
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The Popular Educator, Τόμοι 1-2;Τόμος 12

1867
...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...

A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1795 - 319 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)...

A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1806 - 452 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 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...

A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 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...

The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - 1811 - 508 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....

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 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;...

A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - 1818 - 478 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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