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 14
... shewn to coincide with the point E ; hence the point в coinciding with the point E , and the point c coinciding with the point F , the straight line BC must coincide with the straight line EF ; because if it did not , it would take some ...
... shewn to coincide with the point E ; hence the point в coinciding with the point E , and the point c coinciding with the point F , the straight line BC must coincide with the straight line EF ; because if it did not , it would take some ...
Seite 15
... shewn to be equal to CB , and the angle AFC was shewn to be equal to the angle AGB ; therefore the two triangles BFC , CGB have the two sides BF , FC respectively equal to the two sides CG , GB , and the included angle BFC equal to the ...
... shewn to be equal to CB , and the angle AFC was shewn to be equal to the angle AGB ; therefore the two triangles BFC , CGB have the two sides BF , FC respectively equal to the two sides CG , GB , and the included angle BFC equal to the ...
Seite 18
... shewn to be greater than it which is im- possible . A B II . Let the vertex of one of the triangles , as D , be within the other triangle , ACB . D E F Join CD ; and produce AC , AD , to E and F. Because AC is equal to AD by hyps , and ...
... shewn to be greater than it which is im- possible . A B II . Let the vertex of one of the triangles , as D , be within the other triangle , ACB . D E F Join CD ; and produce AC , AD , to E and F. Because AC is equal to AD by hyps , and ...
Seite 19
... shewn impossible for there to be on the same base AB , and on the same A C D B side of it , two triangles ACB , ADB , having their sides ac , AD terminated in one extremity A of the base equal , and likewise their sides BC , BD ...
... shewn impossible for there to be on the same base AB , and on the same A C D B side of it , two triangles ACB , ADB , having their sides ac , AD terminated in one extremity A of the base equal , and likewise their sides BC , BD ...
Seite 25
... shewn that the angles EBC , EBD are equal to the same three angles ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore the angles ABC , ABD are equal to the angles EBC , EBD . Now , EBC , EBD ...
... shewn that the angles EBC , EBD are equal to the same three angles ; and things that are equal to the same thing are equal to one another ( Ax . 1 ) : therefore the angles ABC , ABD are equal to the angles EBC , EBD . Now , EBC , EBD ...
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.