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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 ... - Σελίδα 1
των Euclides - 1853
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Sessional Papers - Legislature of the Province of Ontario, Τόμος 1

Ontario. Legislative Assembly - 1887
...beget within a lover of the beautiful in nature an uncontrollable desire to enter. The definition of a straight line is " that which lies evenly between its extreme points," or "the shortest distance between two extreme points." Fidelity to this definition guides most persons...

Historic Oddities and Strange Events

Sabine Baring-Gould - 1889 - 323 σελίδες
...points without establishing, in idea, a line between them, indeed, according to Euclid's definition, a. straight line is that which lies evenly between its extreme points, and a line is length without breadth or substance. So, if we conceive of two snails, weestablish a...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...has no magnitude. 2. A Line is length without treadth. 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 has only length and breadth. 6. The Extremities of a Superficies are...

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

Euclid - 1892 - 518 σελίδες
...without breadth. The extremities of a line are points, and the intersection of two lines is a point. 3. A straight line is that which lies evenly between its extreme points. Any portion cut off from a straight line is called a segment of it. 4. A surface is that which has...

Primer of Philosophy

Paul Carus - 1893 - 232 σελίδες
...tendency to regard the path of a ray of light as the prototype of straight lines in geom* Euclid says : "A straight line is that which lies evenly between its extreme points." etry. The fact, however, is that light does not travel in straight lines or on paths of shortest time,...

Colliery Surveying: A Primer Designed for the Use of Students and Colliery ...

Thomas Aloysius O'Donahue - 1896 - 163 σελίδες
...length, breadth, nor thickness. A line is length without breadth. The extremities of a line are points. A straight line is that which lies evenly between its extreme points, and is the shortest distance between any two points, as AB (Fig. 16). CHAP. Ill II same straight line,...

On the Study and Difficulties of Mathematics

Augustus De Morgan - 1898 - 288 σελίδες
...placed upon that surface, we conclude that the surface is plane. Hence the definition of a plane surface is that in which, any two points being taken, the straight line joining these points lies wholly upon the surface. Two straight lines have a relation to one another...

On the Study and Difficulties of Mathematics

Augustus De Morgan - 1898 - 288 σελίδες
...treatises 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,...

English Surnames: Their Sources and Significations

Charles Wareing Endell Bardsley - 1898 - 612 σελίδες
...there may be a beauty in an erection which reminds you in perpetuity of the great Euclidian truth that a straight line is that which lies evenly between its extreme points, but at times it puts one in sober mood to think all the touches of a past time are to fade away, and...

A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Βιβλίο 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 σελίδες
...breadth. 3. The extremities of a line are points, and the intersection of two lines is a point. 4. A straight line is that which lies evenly between its extreme points. Any portion cut off from a straight line is called a segment of it. 5. A surface (or superficies) is...




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