Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

any error involved in the latter theory, it must not only be infinitely small, but must remain infinitely small after all the magnifying processes to which it could possibly be subjected. But there is no error; for, if we suppose that there be an error which we may represent by A, since the aggregate of all the quantities neglected in arriving at the result is infinitely small, that is, as small as we choose, we may choose it to be smaller than A; and, therefore, the error A is greater than the greatest possible error which could be obtained, a manifest absurdity, but one which cannot be avoided as long as A is any thing.

The term direction is introduced into this trea. tise without being defined; but it is regarded as a simple idea, and to be as incapable of definition as length, breadth, and thickness; and this innovation will probably be pardoned, when it is seen how much it contributes to the brevity and simplicity of demonstration, which I have every. where studied.

BENJAMIN PEIRCE.

[ocr errors][merged small][ocr errors]

.

[merged small][ocr errors][ocr errors]
[ocr errors]
[ocr errors]
[ocr errors]

.

[ocr errors]
[ocr errors]

34

37

[ocr errors]

.

[ocr errors]

.

.

To bisect a line (132),

38

To draw a perpendicular to a line (133, 134),

134),

38

To make an arc or angle equal to a given arc or angle (135, 136), 38

To bisect an arc or angle (137, 138),

39

To draw a line parallel to a given line (139),

40
To find the third angle of a triangle (140),

40
To cons act a triangle (141 – 144),

40

To construct a right triangle (145)

41

To construct a parallelogram (146, 147),

41

To find the centre of an arc or circle (148, 149),

41

To draw a tangent to a circle (150, 151),

42

To inscribe a circle in a triangle (152, 153),

42

To describe a segment capable of containing a given angle

(154, 155),

43

To find the common measure of two lines (156); or of two arcs

(157),

44

CHAPTER X.

PROPORTIONAL LINES,

45

Lines divided into equal parts (158),

45

To divide a line into equal parts (159),

45

A line parallel to one side of a triangle divides the other two

proportionally (160 - 162); and the converse (163),

To divide a line into parts proportional to given lines (164, 165), 47

To find a fourth proportional to three lines (165, 166),

48

To divide one side of a triangle into two parts proportional to

the other two sides (167),

To draw a line through a point in an angle so that it may be di-

vided in a given ratio by the point (168, 169),

49

CHAPTER XI.

SIMILAR POLYGONS,

49

Similar polygons and their homologous sides; similar arcs (170), 49

Altitude of parallelogram, of triangle, of trapezoid (171),

50

Cases of similar triangles (172-180),

50

Intersections of lines drawn through the vertex of a triangle

with lines parallel to the base (181, 182),

52

Division of the right triangle into similar triangles by a perpen-

dicular to the hypothenuse (183), , .

53

Leg of a right triangle is a mean proportional between hypoth-

enuse and adjacent segment (184, 187), .

53

[ocr errors]

46

.

.

« ΠροηγούμενηΣυνέχεια »