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 8
... are equal to one another . VIII . Magnitudes that coincide with one another , i.e. exactly fill up the same space , are equal to one an- other . IX . The whole is greater than its part . 8 [ BOOK THE ELEMENTS OF EUCLID . Axioms.
... are equal to one another . VIII . Magnitudes that coincide with one another , i.e. exactly fill up the same space , are equal to one an- other . IX . The whole is greater than its part . 8 [ BOOK THE ELEMENTS OF EUCLID . Axioms.
Seite 14
... coincide with the point E , because AB is equal to DE by hypothesis : Again , the straight line AB coinciding with DE , the straight line AC shall fall on DF , because the angle BAC is equal to the angle EDF by hyps ; and the triangles ...
... coincide with the point E , because AB is equal to DE by hypothesis : Again , the straight line AB coinciding with DE , the straight line AC shall fall on DF , because the angle BAC is equal to the angle EDF by hyps ; and the triangles ...
Seite 18
... coincide with one another . There are three cases , according as the vertex ( i . e . the angular point opposite to the base ) of each of the tri- angles is without the other triangle ; or the vertex D of one of them falls within the ...
... coincide with one another . There are three cases , according as the vertex ( i . e . the angular point opposite to the base ) of each of the tri- angles is without the other triangle ; or the vertex D of one of them falls within the ...
Seite 19
... coincide with one another . Which was to be proved . PROP . VIII . 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 ...
... coincide with one another . Which was to be proved . PROP . VIII . 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 ...
Seite 20
... coincide with the point E , because AB is equal to DE by hyps ; therefore the straight line AB coinciding with the straight line DE , and the triangles falling on the same side of DE , the sides AC , CB must coincide with the sides DF ...
... coincide with the point E , because AB is equal to DE by hyps ; therefore the straight line AB coinciding with the straight line DE , and the triangles falling on the same side of DE , the sides AC , CB must coincide with the sides DF ...
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.