Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and Exercises |
From inside the book
Results 1-5 of 61
Page xi
... figure , the latter gives a picture of it , which is better . Surely in this matter common sense must prevail . It may perhaps be not altogether superfluous here to note that beginners in Geometry must be taught ; and that merely ...
... figure , the latter gives a picture of it , which is better . Surely in this matter common sense must prevail . It may perhaps be not altogether superfluous here to note that beginners in Geometry must be taught ; and that merely ...
Page 1
... figures : it is based on definitions , axioms and postulates : these granted , all the rest follows by pure ... figure is to be effected : ( 2 ) theorems - in which from an hypothesis a specified conclusion is to be demonstrated ...
... figures : it is based on definitions , axioms and postulates : these granted , all the rest follows by pure ... figure is to be effected : ( 2 ) theorems - in which from an hypothesis a specified conclusion is to be demonstrated ...
Page 2
... figure ( 1 ) , the angle may be denoted by a single ( 1 ) A / ( 2 ) E D B letter , placed at the common point : thus ... figure is a part of a plane bounded by a line or lines ; and when these lines are straight it is called a plane ...
... figure ( 1 ) , the angle may be denoted by a single ( 1 ) A / ( 2 ) E D B letter , placed at the common point : thus ... figure is a part of a plane bounded by a line or lines ; and when these lines are straight it is called a plane ...
Page 3
... figure , all points of whose boundary are equally distant from a fixed point within it , is called a circle . Def . The fixed point within a circle , from which all points of its boundary are equidistant , is called its centre . Def ...
... figure , all points of whose boundary are equally distant from a fixed point within it , is called a circle . Def . The fixed point within a circle , from which all points of its boundary are equidistant , is called its centre . Def ...
Page 5
... figure , that AQ , BQ , AP , BP are the longer bars ; and that AO , BO are the shorter . Pierce holes in them at A , Q , B , P , O ; and connect them through these holes by pivots , all freely moveable , except the one at O , which is ...
... figure , that AQ , BQ , AP , BP are the longer bars ; and that AO , BO are the shorter . Pierce holes in them at A , Q , B , P , O ; and connect them through these holes by pivots , all freely moveable , except the one at O , which is ...
Common terms and phrases
ABCD Addenda altitude base bisector bisects centre of similitude chord circum-circle circumf circumference coincide collinear concyclic corners cross-ratio cyclic quadrilateral diag diagonals diam diameter divided draw drawn equal angles equiang Euclid find the Locus fixed circle fixed line fixed point given circle given line given point harmonic conjugates inscribed intersection inverse Join Let ABC magnitudes meet mid point mid pt Note-The NOTE-Use opposite sides pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM-To produced Prop Proposition Proposition 13 Ptolemy's Theorem quad radical axis radii radius ratio rect rectangle rectilineal figure respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents THEOREM THEOREM-If touch triangle ABC variable
Popular passages
Page 251 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 29 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 150 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 91 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 82 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 37 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 44 - 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 84 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 22 - Any two sides of a triangle are together greater than the third side.
Page 87 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...