The text is an introduction to basic geometry concepts essential for drawing from nature, focusing on fundamental definitions such as points, lines, angles, and surfaces. It explains simple geometric constructions and distinctions between different types of lines and angles. The text serves to bridge standard geometric understanding with practical applications for those learning to draw from nature.
PRELIMINARY NOTIONS.
We have reproduced here, in a condensed form, some very elementary notions that are part of the Introduction to our Treatise on Simplified Perspective. This last work will be particularly useful to those who are already well advanced in Drawing, according to ordinary methods, but who wish to practice Drawing from Nature and put themselves in a position to give good advice to beginners.
SOME NOTIONS OF GEOMETRY.
BOARD 1. — Some definitions and very simple constructions, indispensable for the practice of Drawing from Nature.
Geometry. - Extent. - Point. - Surface.
Geometry is a science that deals with the measurement of extent. Extent has three dimensions: length, width, height.
The point, strictly defined as by Geometers, would have no length, width, or height: for practical purposes, consider it as the smallest extent in any measurement.
A surface is defined as an extent having length and width, without height.
Straight, broken, or curved lines, perpendicular, or oblique, Right angles, acute, or obtuse.
A line can be defined as a continuation of points forming a length. There are two types of lines, the straight line and the curved line.
A straight line is defined by Geometers as the shortest path from one point to another. We define it as a line where all points are in the same direction. A line composed of several straight lines is called a broken line.
A line that is neither straight nor composed of straight lines is called a curved line. The points it consists of continually change direction among themselves.
AB (fig. 1) is a straight line; EFGHILK, a broken line; CD a curved line.
When two straight lines meet, they form what is called an angle.
An angle is the amount more or less by which two lines that meet deviate from one another. In an angle, there are the sides and the vertex.
Point B (fig. 4), the meeting point of the two lines CB, AB, is the vertex of the angle they form. BC, AB are the sides of the angle.
An angle is designated by three letters, for example: angle ABC, placing the letter of the vertex in the middle of these three letters. Sometimes only the letter of the vertex is named.
If a line CD (fig. 3) meets another AB, so that the two angles ADG, BDC are perfectly equal, these two angles are called right angles, and the line CD will be called perpendicular, with respect to line AB. It is seen that CD, in relation to AB, does not tilt.
Translation Notes:
- "Géométrie" is translated as "Geometry," referring to the mathematical discipline.
- "Étendue" translates as "Extent," meaning the measurable distance or area.
- "Ligne brisée" is "broken line," indicating a composite line made up of straight segments.