The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1 |
From inside the book
Results 1-5 of 56
Page 2
... angle is the inclination of two lines to one another in a plane , which meet together in a point , but are not in ... third being indifferent . Ex . Of the three angles at the point A ( Fig . I ) , the angle in- cluded by the straight ...
... angle is the inclination of two lines to one another in a plane , which meet together in a point , but are not in ... third being indifferent . Ex . Of the three angles at the point A ( Fig . I ) , the angle in- cluded by the straight ...
Page 13
... angle included by the two sides of the other : then these triangles shall be equal in every respect ; i . e . ( 1 ) the base or third side of the one shall be equal to the base or third side of the other ; ( 2 ) the remaining angles of ...
... angle included by the two sides of the other : then these triangles shall be equal in every respect ; i . e . ( 1 ) the base or third side of the one shall be equal to the base or third side of the other ; ( 2 ) the remaining angles of ...
Page 31
... angle ABC would be equal ( i . 5 ) to the an- gle ACB ; but it is not : therefore AC is not equal to AB . Neither is ... third side . Let ABC be a triangle . Then any two of its sides to- gether shall be greater than the third side ...
... angle ABC would be equal ( i . 5 ) to the an- gle ACB ; but it is not : therefore AC is not equal to AB . Neither is ... third side . Let ABC be a triangle . Then any two of its sides to- gether shall be greater than the third side ...
Page 32
... angle : then these two straight lines shall together be less than the other two sides of the triangle , and shall ... third BE ; to each of these unequals add EC : then BA , AC are greater ( Ax . 4 ) than BE , EC . Again , the two sides CE , ...
... angle : then these two straight lines shall together be less than the other two sides of the triangle , and shall ... third BE ; to each of these unequals add EC : then BA , AC are greater ( Ax . 4 ) than BE , EC . Again , the two sides CE , ...
Page 33
... third . Let A , B , C be the three given straight lines , of which any two are together greater than the third , viz ... angle OFG has been made having its three sides of , FG , GO respectively equal to A , B , C. Which was to be done , : ...
... third . Let A , B , C be the three given straight lines , of which any two are together greater than the third , viz ... angle OFG has been made having its three sides of , FG , GO respectively equal to A , B , C. Which was to be done , : ...
Common terms and phrases
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Popular passages
Page 39 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Page 52 - 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 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Page 11 - 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 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Page 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Page 66 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.