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GEOMETRICAL CONSTRUCTIONS, .
The following constructions are to be made with the Ruler and Compasses only; the Ruler being used for drawing and producing straight lines, the Compasses for describing circles and for the transference of distances.
1. The bisection of an angle.
from a point outside, a given straight line, and
on a given straight line. 4. The construction of an angle equal to a given angle;
of an angle equal to the sum of two given angles, &c. 5. The drawing of a line parallel to another under
various conditions and hence the division of lines
into aliquot parts, in given ratio, &c.
(a) three sides;
7. The drawing of tangents to circles, under various
conditions. 8. The inscription and circumscription of figures in and
about circles; and of circles in and about figures. 7 and 8 may be deferred till the Straight Line and Triangles
have been studied theoretically, but should in all
cases precede the study of the Circle in Geometry. The above constructions are to be taught generally, and illustrated by one or more of the following classes of problems : (a) The making of constructions involving various com
binations of the above in accordance with general (i.e. not numerical) conditions, and exhibiting some of the more remarkable results of Geometry, such as the circumstances under which more than two straight lines pass through a point, or more than
two points lie on a straight line. (B) The making of the above constructions and combi
nations of them to scale (but without the protractor). (y) The application of the above constructions to the
indirect measurement of distances. (8) The use of the protractor and scale of chords, and the
application of these to the laying off of angles, and the indirect measurement of angles.
[Note.--The Association have prefaced their Syllabus by a Logical Introduction, but they do not wish to imply by this that the study of Geometry ought to be preceded by a study of the logical interdependence of associated theorems. They think that at first all the steps by which any theorem is demonstrated should be carefully gone through by the student, rather than that its truth should be inferred from the logical rules here laid down. At the same time they strongly recommend an early application of general logical principles.]
Propositions admitted without demonstration are
more frequently used.
to one another. (d) If equals are added to equals the sums are equal.