The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bücher 11853 |
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Ergebnisse 1-5 von 66
Seite 16
... fore by the prop " the angles CAB , ABC are equal . Hence each of the angles ACB , CAB is equal to the angle ABC ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore the angle ACB is equal to the ...
... fore by the prop " the angles CAB , ABC are equal . Hence each of the angles ACB , CAB is equal to the angle ABC ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore the angle ACB is equal to the ...
Seite 22
... fore these two triangles have the three sides FD , DC , CF respectively equal to the three sides FE , EC , CF. fore they are equal in every respect ( i . 8 ) ; and hence the angle DCF is equal to the angle ECF . Thus the straight line ...
... fore these two triangles have the three sides FD , DC , CF respectively equal to the three sides FE , EC , CF. fore they are equal in every respect ( i . 8 ) ; and hence the angle DCF is equal to the angle ECF . Thus the straight line ...
Seite 29
... fore the angle BCH is greater than the angle ABK or and the angle ACD is equal to the angle вCH , since they are opposite vertical angles : therefore the angle ACD is greater than the angle ABC . ABC ; Hence the exterior angle ACD is ...
... fore the angle BCH is greater than the angle ABK or and the angle ACD is equal to the angle вCH , since they are opposite vertical angles : therefore the angle ACD is greater than the angle ABC . ABC ; Hence the exterior angle ACD is ...
Seite 35
... fore the angle DKH is greater than the angle DнK ; and the greater angle of a triangle is subtended by the greater side ( i . 19 ) : therefore DH is greater than DK . But DF is equal to DH or AC by const " : therefore DF is greater than ...
... fore the angle DKH is greater than the angle DнK ; and the greater angle of a triangle is subtended by the greater side ( i . 19 ) : therefore DH is greater than DK . But DF is equal to DH or AC by const " : therefore DF is greater than ...
Seite 42
... fore the angles AGH , BGH are equal to the angles BGH , GHD . From each of these equals take away the common angle BGH : then the remaining angle AGH is equal ( Ax . 3 ) to the remaining angle GHD . Hence EF cutting the two straight ...
... fore the angles AGH , BGH are equal to the angles BGH , GHD . From each of these equals take away the common angle BGH : then the remaining angle AGH is equal ( Ax . 3 ) to the remaining angle GHD . Hence EF cutting the two straight ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.