Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
From inside the book
Results 1-5 of 39
Page 6
... drawn . A Diagram ( from diagramma , a drawing of lines ) , is the drawing which represents a geometrical figure . The Solution ( from solutio , an unloosening , an explaining ) , of a problem shows how the thing proposed may be done ...
... drawn . A Diagram ( from diagramma , a drawing of lines ) , is the drawing which represents a geometrical figure . The Solution ( from solutio , an unloosening , an explaining ) , of a problem shows how the thing proposed may be done ...
Page 8
... draw various lines which are not mentioned in the hypothesis , the conclusion at which we arrive is altogether dependent on the hypothesis . The fourth kind of evidence is from proof already given ; for what has once been established ...
... draw various lines which are not mentioned in the hypothesis , the conclusion at which we arrive is altogether dependent on the hypothesis . The fourth kind of evidence is from proof already given ; for what has once been established ...
Page 10
... draw Parallel lynes , and how to forme diuersly figures of three sides , and foure sides , according to the varietie ... drawn for whatever is visible must have breadth . A line is measured by the number of units of length contained in ...
... draw Parallel lynes , and how to forme diuersly figures of three sides , and foure sides , according to the varietie ... drawn for whatever is visible must have breadth . A line is measured by the number of units of length contained in ...
Page 12
... drawn from the centre to each of these divisions , the angle formed by every adjacent pair of lines is called an angle of one degree . 16. And the point ( from which the equal lines are drawn ) is called the centre ( kentron , a goad ...
... drawn from the centre to each of these divisions , the angle formed by every adjacent pair of lines is called an angle of one degree . 16. And the point ( from which the equal lines are drawn ) is called the centre ( kentron , a goad ...
Page 15
... drawn from any one point to any other point : 2. That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre at any distance from that centre . The first and ...
... drawn from any one point to any other point : 2. That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre at any distance from that centre . The first and ...
Common terms and phrases
AB² ABCD adjacent angles altitude angle equal angular point Axiom base BC bisected centre circle circumference coincide CON.-Pst Conc construct Deansgate diagonal diameter divided drawn equal bases equal sides equal triangles equil Euclid exterior angle four rt given line given point given st hypotenuse inference interior angles intersect JOHN HEYWOOD join Let the st line BC line CD measure meet miles opposite angles parallel parallelogram perpendicular Plane Geometry produced PROP proposition proved Quæs rectangle rectil rectilineal angle rectilineal figure right angles Scale of Equal side AC sides and angles square straight line surface Syene Theodolite theorem thing vertex Wherefore
Popular passages
Page 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 17 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Page 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Page 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Page 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.
Page 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.