[alogo] Cissoid of Diocles

Below we describe the cissoid, constructed through the [implicit function tool]. The figure depends on number (a). It depends also from the frame ABCD, which restricts the curve. The description is created automatically by slecting the menu-item [File-Image\Describe Schemes]. Look at Diocles.html for a different construction of the curve, as a geometric locus.


[0_0] [0_1]
[1_0] [1_1]
[2_0] [2_1]
[3_0] [3_1]
[4_0] [4_1]


<-- SCHEME-START -- >
<-- TOOL -- > Define a Number-Object:
Type somewhere the number { 2.1000}. Then press the RETURN key.
<-- TOOL -- > Select the Point-tool: (3rd-Button), (Shortcut: Ctrl+E).
Click at P to define a point there.
<-- TOOL -- > Define a Formula-Object:
Type somewhere the text-box {formula x^3-y^2*(2.*a-x)}. Then select it and press the RETURN key.
<-- TOOL -- > Select the Screen-Rectangle-tool: (9th-Button/2nd-Button from below).
Click at A, drag ... , release at C to define the screen-rectangle o = (ABCD).
<-- TOOL -- > Select the Addition-operator {+} (right toolbar):
Click on the two number-objects { 2.1000} and { 2.1000} to find their sum = {{ 2.1000}+{ 2.1000}} (a new number-object).
<-- TOOL -- > Select the Cartesian-Coordinates-tool: (Measures-Menu\Cartesian Coordinates_ ).
Click on P in order to define the group of its Cartesian coordinates x= ..., y=... .
<-- TOOL -- > Select the selection-tool: (1st-Button), (shortcut: Ctrl+1).
Double-click on number { 4.2000} holding down simultaneously the key F2, in order to define point Q with this coordinate on the x-axis.
<-- TOOL -- > Evaluate a Formula for a list of arguments. For this:
Right-click on Formula {x^3-y^2*(2.*a-x)} and select the menu-item {Activate}. Then click on each number of the list: { 1.6531} { -1.3469} { 2.1000}, getting { -0.1036}.
<-- TOOL -- > Select the Parallel-to-tool (line): (6th-Button/4th-Menu-item), (Shortcut: Ctrl+Q).
Click on AB. Then click at Q, to define the parallel line c from Q to AB.
<-- TOOL -- > Select the tool of Implicit-Restricted-Functions: (14th-Button/last item).
Click on point P, then on the number-object { -0.1036} and finally on screenrect o in order to find all points point P (inside the rectangle) such that z({ -0.1036}) is zero.
<-- TOOL -- > Select the Point-tool: (3rd-Button), (Shortcut: Ctrl+E).
Click next to E, holding down the CTRL key, to define an intersection point of screenrect o and line c .
Click next to F, holding down the CTRL key, to define an intersection point of screenrect o and line c .
<-- TOOL -- > Select the Segment-tool: (5th-Button), (Shortcut: Ctrl+Alt+S).
Click at E, drag ... , release at point F, to define segment g=EF.
<-- SCHEME-END -- >



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