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" A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 1
av Euclides - 1853
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...v -^v~' II See Notes. A line is length without breadth. III. The extremities of a line are points. A straight line is that which lies evenly between its extreme points. V. A superficies is that which hath only length and breadth. The extremities of a superficies are lines. VII. A plane superficies...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...which hath no parts, or which hath no magnitude. H. See Notes. A line is length without breadth. III. The extremities of a line are points. IV. A straight...extreme points. . '. .. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volum 10

1816
...fnperficies are therefore lines, and the interactions of fupcrficies with one another are alfo lines. 5. A PLANE SUPERFICIES is that in which any two points being taken, the ftraight line between them lies wholly in that fupcrficies. 6. A PLANE RECTILINEAL ANGLE is the inclination...
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A Treatise on Surveying: Containing the Theory and Practice : to which is ...

John Gummere - 1817 - 206 sider
...between any two points. 4. A superficies or surface has length and breadth, but not thickness^ ^1 '' ' 6. A plane superficies is that in which any two points being taken, the straight line which joins them lies wholly in that superficies. 7. A plane rectilineal angle is the inclination of...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...superficies are lines ; and the intersec" tions of one superficies with another are also lines." V. A plane superficies is that in which any two points being taken, thp straight line between them lies wholly in that superficies. VI. A plane rectilineal angle is the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...hath no magnitude. 2. A line is length without breadth. 3. the extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. 5. A superficies is that which hath only length and breadth. 6. The extremities of a superficies are...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...which hath no parts, or which hath no See Note*, magnitude. II. A line is length without breadth. III. The extremities of a line are points. IV. A straight...its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies...
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Elements of Geometry: With Notes

John Radford Young - 1827 - 208 sider
...by any definition, a better notion of it than the mere mention of its name suggests. Euclid says, " A straight line is that which lies evenly between its extreme points*;" a definition which is both unsatisfactory and useless. Others, following Archimedes, define it as "the...
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On the study and difficulties of mathematics [by A. De Morgan].

Augustus De Morgan - 1831
...on that subject. A point is defined to be that " which has no parts, and which has no magnitude ;" a straight line is that which " lies evenly between its extreme points." Now, let any one ask himself whether he could have guessed what was meant, if, before he began geometry,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...lies evenly between its extreme points. V. A superficies is that which hath only length and brendth. VI. The extremities of a superficies are lines. VII....plane superficies is that in which any two points be- Sw N. ing taken, the straight line between them lies wholly in that superficies. VIII. " A plane...
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