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 15
Euclides Henry Judge Hose. PROP . V. THEOR . If a triangle be isosceles : then ( 1 ) the angles at the base shall be equal ; ( 2 ) if the equal sides be produced , the angles on the other side of the base shall be equal . Let the ...
Euclides Henry Judge Hose. PROP . V. THEOR . If a triangle be isosceles : then ( 1 ) the angles at the base shall be equal ; ( 2 ) if the equal sides be produced , the angles on the other side of the base shall be equal . Let the ...
Seite 19
... THEOR . If two triangles have the three sides of the one respectively equal to the three sides of the other : then these triangles shall be equal in every respect , i . e . ( 1 ) the three angles of the one shall be respectively equal ...
... THEOR . If two triangles have the three sides of the one respectively equal to the three sides of the other : then these triangles shall be equal in every respect , i . e . ( 1 ) the three angles of the one shall be respectively equal ...
Seite 25
... THEOR . If at a point in a straight line , two other straight lines , on the opposite sides of it , make with it the adja- cent angles together equal to two right angles : then these two straight lines shall be in one straight line . At ...
... THEOR . If at a point in a straight line , two other straight lines , on the opposite sides of it , make with it the adja- cent angles together equal to two right angles : then these two straight lines shall be in one straight line . At ...
Seite 28
... THEOR . If one side of a triangle be produced : then the exterior angle shall be greater than either of the in- terior and opposite angles . Let ABC be a triangle , and let one of its sides BC be produced to D. Then the exterior angle ...
... THEOR . If one side of a triangle be produced : then the exterior angle shall be greater than either of the in- terior and opposite angles . Let ABC be a triangle , and let one of its sides BC be produced to D. Then the exterior angle ...
Seite 29
... THEOR . Any two angles of a triangle shall be together less than two right angles . Let ABC be any triangle . Then any two of its angles shall be together less than two right angles . Produce one of its sides BC to D. Because the side ...
... THEOR . Any two angles of a triangle shall be together less than two right angles . Let ABC be any triangle . Then any two of its angles shall be together less than two right angles . Produce one of its sides BC to D. Because the side ...
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.