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 27
Page 12
... equi- lateral triangle DAB ; from the equals DL , DG , take away the equals DA , DB : then the remainders are equal ( Ax . 3 ) , or AL is equal to BG . But BC also is equal to BG ; and things that are equal to the same thing are equal ...
... equi- lateral triangle DAB ; from the equals DL , DG , take away the equals DA , DB : then the remainders are equal ( Ax . 3 ) , or AL is equal to BG . But BC also is equal to BG ; and things that are equal to the same thing are equal ...
Page 16
... equi- angular . Let ABC be an equilateral triangle . Then it shall also be equiangular . B A C Since the triangle ABC is equi- lateral , the side AB is equal ( Def . 24 ) to the side AC ; and therefore by the prop " , the angles at the ...
... equi- angular . Let ABC be an equilateral triangle . Then it shall also be equiangular . B A C Since the triangle ABC is equi- lateral , the side AB is equal ( Def . 24 ) to the side AC ; and therefore by the prop " , the angles at the ...
Page 17
... equi- lateral . Let ABC be an equiangular tri- angle . Then it shall also be equi- lateral . Since the triangle ABC is equian- gular , the angle ABC is equal to the angle ACB ; and therefore by the prop " the sides opposite to them ...
... equi- lateral . Let ABC be an equiangular tri- angle . Then it shall also be equi- lateral . Since the triangle ABC is equian- gular , the angle ABC is equal to the angle ACB ; and therefore by the prop " the sides opposite to them ...
Page 21
... equi- lateral triangle ABC ; bisect ( i . 9 ) the angle ACB by the straight line CD , cutting AB in D. Then AB shall be bisected in the point D. C D B Because AC is equal to CB , since they are sides of the equilateral triangle ABC , CD ...
... equi- lateral triangle ABC ; bisect ( i . 9 ) the angle ACB by the straight line CD , cutting AB in D. Then AB shall be bisected in the point D. C D B Because AC is equal to CB , since they are sides of the equilateral triangle ABC , CD ...
Page 137
... PROB . About a given circle to circumscribe a triangle equi- angular to a given triangle . Let ABC be the given circle , and DEF the given tri- angle . It is required about the circle ABC to N 3 BOOK IV . ] 137 PROPOSITIONS I. II . III .
... PROB . About a given circle to circumscribe a triangle equi- angular to a given triangle . Let ABC be the given circle , and DEF the given tri- angle . It is required about the circle ABC to N 3 BOOK IV . ] 137 PROPOSITIONS I. II . III .
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.