Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
From inside the book
Results 1-5 of 13
Page 7
... contained in it , reckoned in square units , as square inches , square feet , & c . A locus in Plane Geometry is a straight line , or a plane curve , every point of which , and none else , satisfies a certain condition . NATURE OF ...
... contained in it , reckoned in square units , as square inches , square feet , & c . A locus in Plane Geometry is a straight line , or a plane curve , every point of which , and none else , satisfies a certain condition . NATURE OF ...
Page 9
... contained in both the propositions , with which common thing , as with a test or standard , the other two things are compared : we say― All the triangle is in the circle , All the square is in the triangle , therefore , All the square ...
... contained in both the propositions , with which common thing , as with a test or standard , the other two things are compared : we say― All the triangle is in the circle , All the square is in the triangle , therefore , All the square ...
Page 10
... contained in it ; -as , 5 inches ; 9 feet ; 13 miles .. 3 . The Extremities ( extremus , outermost ) , of a line are points . 4. A straight line is that which lies evenly between its extreme points . " A straight line is the shortest ...
... contained in it ; -as , 5 inches ; 9 feet ; 13 miles .. 3 . The Extremities ( extremus , outermost ) , of a line are points . 4. A straight line is that which lies evenly between its extreme points . " A straight line is the shortest ...
Page 11
... contained within its boundaries ; -as , 4 square inches ; square feet ; 13 square yards , & c . 8. A plane angle ( angulus , a corner ) , is the inclination of two lines to each other in a plane , which meet together in the same point ...
... contained within its boundaries ; -as , 4 square inches ; square feet ; 13 square yards , & c . 8. A plane angle ( angulus , a corner ) , is the inclination of two lines to each other in a plane , which meet together in the same point ...
Page 12
... contained by one line , which is called the circumference ( circumferre , to carry round ) , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . Any portion ...
... contained by one line , which is called the circumference ( circumferre , to carry round ) , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . Any portion ...
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.