The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Bücher 11853 |
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Seite 3
... perpendicular to the other . XI . An obtuse angle is an angle which is greater than a right angle . XII . An acute angle is an angle which is less than a right angle . XIII . The boundary is the extremity of any thing . XIV . A figure ...
... perpendicular to the other . XI . An obtuse angle is an angle which is greater than a right angle . XII . An acute angle is an angle which is less than a right angle . XIII . The boundary is the extremity of any thing . XIV . A figure ...
Seite 23
... perpendicular to a given straight line of indefinite length , from a given point without it . Let AB be the given ... perpendicular to AB . On the side of AB opposite to c take any point D ; join CD ; and with centre c and radius CD ...
... perpendicular to a given straight line of indefinite length , from a given point without it . Let AB be the given ... perpendicular to AB . On the side of AB opposite to c take any point D ; join CD ; and with centre c and radius CD ...
Seite 24
... perpendicular to the given straight line AB . Which was to be done . " PROP . XIII . THEOR . The adjacent angles which one straight line makes with another on the same side of it shall either be two right angles , or be together equal ...
... perpendicular to the given straight line AB . Which was to be done . " PROP . XIII . THEOR . The adjacent angles which one straight line makes with another on the same side of it shall either be two right angles , or be together equal ...
Seite 83
... perpendicular drawn to this side produced from the opposite angular point . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB ; let BC , one of the sides including it , be produced to D ; and from the opposite angular ...
... perpendicular drawn to this side produced from the opposite angular point . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB ; let BC , one of the sides including it , be produced to D ; and from the opposite angular ...
Seite 84
... perpendicular AE be drawn ( i . 12 ) from the opposite angular point A. Then the square of AC shall be less than the squares of AB , BC by twice the rectangle CB , BE . There are two cases according as the perpen- dicular AE does not ...
... perpendicular AE be drawn ( i . 12 ) from the opposite angular point A. Then the square of AC shall be less than the squares of AB , BC by twice the rectangle CB , BE . There are two cases according as the perpen- dicular AE does not ...
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.